Study of Laser Induced Fluorescence Spectrum of Atoms Using ...

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Study of Laser Induced Fluorescence Spectrum of Atoms Using ...

Study of Laser Induced

Fluorescence Spectrum of Atoms

Using Optical Nanofibers

Manoj Das

The University of

Electro–Communications

MARCH 2011


Study of Laser Induced

Fluorescence Spectrum of Atoms

Using Optical Nanofibers

by

Manoj Das

A thesis submitted in partial fulfillment of the

requirements for the award of the degree of

Doctor of Philosophy

to

Department of Applied Physics and Chemistry

Graduate School of Electro–Communications

The University of Electro–Communications

Chofu–Shi, Tokyo, Japan

March, 2011


Study of Laser Induced

Fluorescence Spectrum of Atoms

Using Optical Nanofibers

APPROVED BY SUPERVISORY COMMITTEE:

CHAIRPERSON: PROF. Kohzo Hakuta

MEMBER: PROF. Chikashi Yamada

MEMBER: PROF. Shinichi Watanabe

MEMBER: PROF. Ken-ichi Nakagawa

MEMBER: ASSOCIATE PROF. Tsuyoshi Okuno

MEMBER: ASSOCIATE PROF. Norihito Sogoshi


c○2011 – Manoj Das

All rights reserved.


Dedicated to my Father, Mother and my Sister


Abstract

Fluorescence of atoms has been the subject of interest in quantum optical measurements

for many years. The atomic fluorescence is routinely used as a tool to detect

atoms, to generate photons and to generate non-classical states of light. One of the

widely used methods to investigate the atomic fluorescence is laser-induced fluorescence

spectroscopy. This thesis presents the development of optical nanofibers as a

tool for the measurement of fluorescence spectrum of atoms.

Optical nanofibers are ultrathin optical fibers, with diameters less than the propagation

wavelength of the fiber, with a silica core and a vacuum clad. Such optical

nanofibers can support only the single propagating guided-mode. The guided-modes

of the nanofiber is confined in the transverse direction of the nanofiber and a part

of the propagating field lies outside the fiber, in the evanescent region of the fiber.

The mode density of the electromagnetic field is modified by the nanofiber. Due to

the modification of mode density, the spontaneous emission of atoms is modified by

the optical nanofibers and the confinement of the guided-modes results in a strong

channeling of spontaneous emission of atoms into the guided-modes of the nanofiber.

Such a property of nanofibers can be used to study fluorescence of atoms around the

nanofiber.

Optical nanofibers are prepared by the adiabatic tapering of single-mode optical

fibers. Our experiments are performed by overlapping cold Cesium atoms, from a

magneto-optical trap (MOT), with the optical nanofiber and observing the fluorescence

through the guided-modes of the nanofiber. The nanofiber suppresses with high

probability any coupling of scattering light from the excitation laser into the guidedmodes

and high coupling efficiency of fluorescence into the guided-modes enables us to

measure the fluorescence spectrum of atoms present around the nanofiber with a good

signal-to-noise ratio. In this thesis, we demonstrate the measurement of laser induced

fluorescence (LIF) emission spectra of strongly driven atoms using optical nanofibers.

For the fluorescence emission spectrum measurements, we develop and demonstrate a

new sensitive and high resolution method consisting of optical heterodyne technique


and photon correlation spectroscopy. The key point of the method is to extract the

information of first-order field correlation function from the measured second-order

intensity correlation function. The Fourier transform of the field correlation function

then gives the fluorescence emission spectrum.

The atoms emitting fluorescence in the guided-modes of the nanofiber lie very close

to the nanofiber surface and are subjected to atom-surface interactions. It has been

reported in earlier experiments on nanofiber, that such surface interactions can be

modified by irradiating the MOT-atoms overlapped with the nanofiber with UV lasers.

After such irradiations, MOT-atoms are kept from falling into the surface-potential

and behave almost like free-space atoms around the nanofiber. We first perform our

fluorescence spectra measurements under this free-atom conditions. The observed

excitation spectrum lineshape shows a free-atom like Lorentzian behavior, with a

very small tail in the red-detuned side (red-tail). The red-tail has been attributed

to photoassociation process, due to atoms making transition from free ground states

to bound excited states of the surface potential. Under this conditions, the emission

spectra measured for on-resonant and off-resonant excitations show the well-known

three-peak Mollow-triplet spectrum of free-space two-level atoms. The observation

confirms that the near surface atoms behave like free-space atoms. Also, the quantitative

agreement between the observed spectra with the theoretical calculations

demonstrates the validity of the optical nanofiber method for measuring fluorescence

emission spectrum of atoms.

As mentioned above, since we are observing near-surface atoms, fluorescence measurements

based on optical nanofibers may become a unique tool to probe atomsurface

interactions. In earlier experiments using nanofiber, signatures of atomsurface

interaction have been observed in the excitation spectrum of atoms, in the

form of a broad red-tail. The lineshape of the excitation spectrum is understood as a

result of a process where atoms approaching the nanofiber surface fall into the shallow

surface potential, forming long-range atom-surface bound states. In this thesis,

we have systematically investigated the evolution of the lineshape of the excitation

spectrum from a Lorentzian shape to a broad red-tail condition. The evolution of the


spectrum lineshape has been attributed to the changing nanofiber surface condition.

The spectrum shape is found to depend on the flux of background Cs-atoms. We

speculate that this might be due to the adsorption of hot background atoms onto

the nanofiber surface, which changes the surface condition of the nanofiber locally

and helps in loading of cold MOT-atoms into the shallow surface potential. We have

found that the effect of UV laser irradiation is to photoionize the MOT-atoms, and

the generated photoelectrons might help in the desorption of adsorbed atoms on the

surface. We discuss the roles of adsorption and desorption of atoms on the surface

conditions. We have shown that such changing surface condition can be controlled

by adjusting the hot background atom flux and the UV laser intensity. Under such

controlled surface condition, we have measured the emission spectrum. The observed

emission spectrum under the broad red-tail condition can be explained only by including

the surface interactions. We also discuss qualitatively the phonon-mode density

for nanofiber at room temperature and the phonon-mediated decay of atoms in the

surface potential.

This work may open up the way for using optical nanofibers as a tool to investigate

the laser-induced fluorescence spectrum of strongly driven atoms, and to study atomsurface

interactions. In the future, we hope to create optical dipole traps around the

nanofibers by introducing trap laser lights through the guided-modes and perform

fluorescence measurements of these trapped atoms.


Table of Contents

List of Figures

v

1 Introduction 2

1.1 Light Scattering and Resonance Fluorescence . . . . . . . . . . . . . . 2

1.2 Laser Induced Fluorescence (LIF) Spectroscopy . . . . . . . . . . . . 4

1.3 Optical Nanofibers for LIF Spectroscopy . . . . . . . . . . . . . . . . 7

1.3.1 Mode Structure in Optical Nanofibers . . . . . . . . . . . . . . 9

1.3.2 Modified Spontaneous Emission of Atoms Around the Nanofiber 11

1.4 Optical Nanofibers as a Tool for Probing Atom-Surface Interactions . 17

1.5 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2 Experimental Techniques 24

2.1 Experimental Realization of Nanofiber: Tapered Optical Fiber Technology

................................... 25

2.2 The Magneto-Optical Trap (MOT) System . . . . . . . . . . . . . . . 31

2.2.1 The Vacuum System . . . . . . . . . . . . . . . . . . . . . . . 31

2.2.2 The MOT Laser Systems: Distributed Feedback (DFB) Lasers 33

2.2.3 Laser Stabilization and Frequency Control . . . . . . . . . . . 38

i


2.2.4 Optical Setup and Magnetic-Field System for the MOT . . . . 45

2.3 Optical Nanofiber with MOT Cold Atoms . . . . . . . . . . . . . . . 50

2.4 The Excitation Laser Systems and Their Frequency Stabilization . . . 51

2.5 The Detector, Timing and Photon-Correlator Systems . . . . . . . . . 58

2.6 Density and Temperature of MOT-atoms . . . . . . . . . . . . . . . . 62

3 Fluorescence Spectrum of Strongly Driven Atoms 66

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.2 LIF Excitation Spectrum Measurements : Experimental Procedures

andResults ................................ 68

3.3 Atom-Number Estimations . . . . . . . . . . . . . . . . . . . . . . . . 73

3.4 LIF Emission Spectrum Measurements : Experimental Procedures . . 75

3.4.1 Optical Heterodyne Technique . . . . . . . . . . . . . . . . . . 76

3.4.2 Photon Correlation Spectroscopy . . . . . . . . . . . . . . . . 77

3.4.3 Combined Heterodyne and Correlation Spectroscopy . . . . . 80

3.5 LIF Emission Spectrum Measurements : Results . . . . . . . . . . . . 86

3.5.1 On-Resonant Excitations . . . . . . . . . . . . . . . . . . . . . 86

3.5.2 Off-Resonant Excitations . . . . . . . . . . . . . . . . . . . . . 88

3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4 Probing Atom-Surface Interactions Using Optical Nanofibers 96

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.2 LIF Spectrum Measurements of Surface-Bound Atoms: Experimental

Procedures................................. 97

4.3 LIF Spectrum Measurements of Surface-Bound Atoms: Results . . . . 99

4.3.1 LIF Excitation Spectrum Measurements: Experimental Preparations

and Results . . . . . . . . . . . . . . . . . . . . . . . . 99

4.3.2 Effect of UV laser irradiation . . . . . . . . . . . . . . . . . . 101

4.3.3 Hot atom effect on the surface . . . . . . . . . . . . . . . . . . 103


4.3.4 LIF Emission Spectrum Measurements : Experimental Preparations

and Results . . . . . . . . . . . . . . . . . . . . . . . . 106

4.4 LIF Spectrum Measurements: Analysis and Discussions . . . . . . . . 110

4.4.1 Atom-Surface Bound States . . . . . . . . . . . . . . . . . . . 110

4.4.2 Phonon-Mediated Loading in the Surface-Potential . . . . . . 115

4.4.3 Effects of UV Laser Irradiation of MOT-Atoms . . . . . . . . 119

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5 Conclusions and Future Extensions of the Present Work 128

5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.2 Future Extensions of the Present Work . . . . . . . . . . . . . . . . . 131

References 136

A Expressions for the Correlation Functions 150

B Optical-Heterodyne Technique Measurements 154

C DFB Feedback-Circuit Details 158

D Development of a Glass-Cell MOT System 160

Acknowledgements 166

Author Biography 170

List of Publications Related to the Thesis 170


List of Figures

1.1 Schematic diagram of a resonance fluorescence experiment. . . . . . . 3

1.2 Schematic diagram showing the single mode propagation of field through

the guided mode of the nanofiber. . . . . . . . . . . . . . . . . . . . . 9

1.3 Modified spontaneous emission around the nanofiber. . . . . . . . . . 14

1.4 Coupling of spontaneous emission into the guided modes. . . . . . . . 15

1.5 Surface-induced potentials for ground and excited-state Cesium atoms

D 2 transition. ............................... 19

2.1 Nanofiber preparation technique. . . . . . . . . . . . . . . . . . . . . 27

2.2 Characteristics of nanofibers. . . . . . . . . . . . . . . . . . . . . . . . 29

2.3 Photograph of the vacuum system . . . . . . . . . . . . . . . . . . . . 32

2.4 Photograph of the DFB laser system . . . . . . . . . . . . . . . . . . 34

2.5 Characteristics of cooling DFB laser . . . . . . . . . . . . . . . . . . . 35

2.6 Characteristics of repump DFB laser . . . . . . . . . . . . . . . . . . 37

2.7 The Cesium D 2 transitions . . . . . . . . . . . . . . . . . . . . . . . . 40

2.8 DFB laser locking system . . . . . . . . . . . . . . . . . . . . . . . . 40

2.9 The cooling DFB laser SAS characteristics . . . . . . . . . . . . . . . 41

2.10 The locking error signal of the cooling laser . . . . . . . . . . . . . . . 42

2.11 The error signal of the cooling DFB laser under locked condition . . 43

v


2.12 The frequency stabilty measurements of the cooling laser . . . . . . . 43

2.13 The SAS signal and the long term stability of the repump laser . . . 46

2.14 Arrangement of the optics for MOT . . . . . . . . . . . . . . . . . . . 47

2.15 Schematic diagram and photograph of the MOT set-up . . . . . . . . 49

2.16 Nanofiber installation into the vacuum chamber . . . . . . . . . . . . 52

2.17 Optical transitions to which the reference and the excitation lasers are

locked ................................... 54

2.18 SAS signal of the excitation laser . . . . . . . . . . . . . . . . . . . . 55

2.19 Schematic diagram of the phase-locking setup . . . . . . . . . . . . . 55

2.20 The phase-locked beat-signal between excitation lasers . . . . . . . . 56

2.21 Schematic diagram of the timing circuit for generating timing signals

for the experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

2.22 Density measurements of MOT-atoms . . . . . . . . . . . . . . . . . . 63

3.1 Experimental setup for measuring opposite-end photon correlations . 69

3.2 Experimental setup for the excitation spectrum measurements . . . . 70

3.3 Measured opposite-end correlations . . . . . . . . . . . . . . . . . . . 74

3.4 Theoretical plot of the first- and second-order correlation functions . 79

3.5 Theoretical plot of fluorescence emission spectra . . . . . . . . . . . . 84

3.6 Experimental setup for LIF emission spectrum measurements . . . . . 85

3.7 One-end photon correlation measurements with OHD technique . . . 87

3.8 On-resonance fluorescence emission spectra . . . . . . . . . . . . . . . 89

3.9 Off-resonant fluorescence emission spectra . . . . . . . . . . . . . . . 90

4.1 Schematic of the experimental setup for probing atom-surface interactions

.................................... 98

4.2 Measured fluorescence excitation spectra: Surface-effects . . . . . . . 100

4.3 Effect of UV laser irradiation . . . . . . . . . . . . . . . . . . . . . . 102

4.4 Time dependence of the on-resonant fluorescence as a function of the

dispenser current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.5 Emission spectrum measurements : Settings for the excitation laser . 106


4.6 Emission spectrum measurements : Photon correlation measurements

with heterodyne technique . . . . . . . . . . . . . . . . . . . . . . . . 107

4.7 Emission spectra : Surface effects . . . . . . . . . . . . . . . . . . . . 109

4.8 Schematic diagram showing the bound states of atoms in the surface

induced potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

4.9 Calculated phonon-mediated decay rates . . . . . . . . . . . . . . . . 116

4.10 Energy level diagram for a Cs-atom near a silica surface . . . . . . . . 119

5.1 Schematic diagram of atom trapping around a nanofiber using a twocolordipoletrap

............................. 132

B.1 Experimental set-up for the heterodyne technique . . . . . . . . . . . 155

B.2 Beat signal between two lasers for a fixed signal power and different

LOpowers................................. 155

B.3 Sensitivity tests of the heterodyne technique using phase sensitive detection...................................

156

C.1 Feedback circuit used for the DFB cooling and repump lasers. . . . . 158

D.1 Schematic diagram of the glass-cell MOT system . . . . . . . . . . . . 162

D.2 Photograph of the glass-cell MOT system and the MOT-fluorescence 163


chapter 1

INTRODUCTION

1.1 Light Scattering and Resonance Fluorescence

Scattering of light by an atom is one of the processes of atom-light interaction where

one photon disappears and a new photon appears. A basic light-scattering experiment

consists of a scattering region where the atoms to be investigated are illuminated by

a parallel beam of light, and a detector that measures the scattered intensity. This

involves a destruction of photon from the incident beam and creation of photon in

the scattered radiation. The light scattering is thus a second-order process since two

interactions of the radiation field and the atomic electrons take place. Scattering

occurs for all values of the incident frequency relative to the transition frequencies of

the scattering atoms. Scattering of light by atoms is widely used to study not only

fundamental light-matter interactions but also for applications like quantum information

science and quantum computing. Especially resonant scattering where the

incident frequency lies close to an atomic transition frequency has been the subject

of interest in quantum optical measurements for many years [1, 2, 3]. This is particularly

because of the strong scattering intensity in resonance conditions which favors

2


1.1. Light Scattering and Resonance Fluorescence 3

Excitation Laser

Atom

Detector

Figure 1.1: Schematic setup of a resonance fluorescence experiment.

experiments involving a single or a small number of atoms. A schematic diagram of

the resonance fluorescence experiment is shown in Fig. 1.1. The resonant fluorescence

is routinely used as a tool to detect atoms, to generate photons and to generate

non-classical states of light [1, 2, 3, 4].

The resonant light scattering which is commonly known as resonance fluorescence

consists of two main contributions, the elastic scattering and the inelastic scattering

components depending on the intensity of the incident driving light field [1, 2]. If

the driving field is monochromatic and the excitation intensity is low compared to

the saturation intensity of the atom, the atom absorbs a photon at the excitation

frequency and reemits it at the same frequency as a consequence of conservation of

energy. The spectral width of the fluorescent light is therefore very narrow and the

scattering is known as elastic scattering. The situation changes completely when the

excitation intensity increases and the Rabi frequency associated with the driving field

becomes comparable to or larger than the atomic linewidth. At such intensity levels

where the atoms are strongly driven, the Rabi oscillations show up as modulation

of the quantum dipole moment and sidebands start emerging in the spectrum of the

emitted radiation. This is the inelastic scattering component or the so called dynamic

Stark splitting and is an important feature of atom-light interactions.


Chapter 1. Introduction 4

1.2 Laser Induced Fluorescence (LIF) Spectroscopy

One of the widely used method to investigate the atomic fluorescence is laser-induced

fluorescence (LIF) spectroscopy. The LIF spectroscopy may be categorized into two

methods. One is the excitation spectroscopy and the other is emission spectroscopy

[4]. The excitation spectroscopy measures the fluorescence radiation from emitters by

tuning the laser wavelength around atomic resonance; on the other hand the emission

spectroscopy measures the spectrum of the emitted fluorescence radiation by fixing the

excitation laser wavelength. Although both the excitation and the emission spectra

give complimentary information, the knowledge of both the spectrum is essential to

get a complete understanding of the laser induced fluorescence.

LIF has a large range of applications in spectroscopy. LIF serves as a sensitive

monitior for the absorption of laser photons in fluorescence excitation spectroscopy

to determine absorption coefficients or number density of absorbing species [5]. The

high sensitivity of excitation spectroscopy is used to monitor minute concentrations

of radicals and short-lived intermediate products in chemical reactions [6, 7]. Apart

from measurements of small concentrations, detailed information on the internal state

distribution of products invloved can be extracted, since the fluorescence signal is

proportional to the number of absorbing atoms/molecules in a particular state to

which the excitation laser is resonant [8]. In case of atoms, if the excitation transition

is a closed cycle transition, that is a true two level system, the atoms may be excited

many times while it flies through the laser beam. This increases the excitationfluorescence

cycles and lots of photon can also be generated from a single atom. This

allows single atom detection. This principle can be also be used for molecules, where

molecular transitions can be effectively a two level transition due to the presence

of collisions with other solvent molecules which can bring the molecule back to its

initial level. This allows the detection of many photons per second from a single

molecule. This method is used for molecules diluted in solutions or in solids, where

single molecules can be excited if the focused laser beam diameter is smaller than the

average distance between the molecules. Thus LIF technique is widely used for single


1.2. Laser Induced Fluorescence (LIF) Spectroscopy 5

atom and molecule detection in chemistry and biology [6, 7, 9, 10, 11].

LIF spectroscopy is also well suited to gain information on molecular states if the

fluorescence spectrum excited by a laser on a selected absorption transition is dispersed

by a spectrum analyzer as in the measurement of LIF emission spectrum [12].

Molecular spectroscopy by LIF measurement is an important area of spectroscopy

[13, 14, 15]. The fluorescence spectrum emitted from a selectively populated rovibronic

(rotational-vibrational states changes simultaneously due to rovibronic coupling)

level consists of all allowed transitions to lower levels. The frequency differences

of the fluorescence lines immediately yield the energy spacing of the vibrational

levels. The Doppler width associated with the temperature of the atoms/molecules

can be reduced in the LIF spectroscopy by the use of cold atoms/molecular systems.

The large intensities available for many single mode narrow linewidth lasers allow

achievement of large population densities in the excited states of molecules. This

results in high intensities of the fluorescence lines and enables detection even of transitions

with very small Franck-Condon factors. The fluorescence lines may therefore

be measured with sufficiently high signal-to-noise ratio up to very high vibrational

levels. The potential curve of the diatomic molecule can then be determined by the

measured energies using standard modelling methods [16, 17]. Since the energy levels

associated with the potential curve can be determined from the wavenumber of the

fluorescence lines, the potential can be constructed for the highest measured vibrational

levels/quantum numbers. In some cases, potential curves can be plotted up

to just below the dissociation limit [18, 19]. The study of potentials based on LIF

measurement is not only valid for molecular vibrational levels but can also be extended

to study surface potentials like atoms near some surface where the atoms can

be bound in the atom-surface bound states [20, 21]. The study of motional states of

atoms trapped in an optical molasses potential has been performed by measuring the

LIF spectrum of the atoms [22, 23]. The fluorescence studies can be extended to investigate

atoms trapped in an optical dipole potential. Moreover, such LIF spectrum

measurements can be used to extract information regarding the collision processes

between the molecules, which results in the transferring of molecules in a particular


Chapter 1. Introduction 6

vibrational level to different levels [24].

Among the two LIF measurement methods as discussed above, the excitation spectroscopy

is rather extensively used in various applications compared to the emission

spectroscopy. This is because the excitation spectroscopy not only provides high resolution,

due to the development of single-mode narrow linewidth lasers, but also gives

high sensitivity due to the integration of spectrally distributed fluorescence photons.

The LIF emission spectrum, which measures the frequency distribution of the emitted

fluorescence can achieve a resolution of several GHz, using conventional spectrometers

like grating spectrometer or Fourier transform infrared interferometer (FTIR).

But, measurements requiring resolution better than natural linewidth of atoms (few

MHz), the above mentioned spectrometers cannot be used. Optical heterodyne based

measurement can provide high resolution, where the fluorescence signal is mixed with

a narrow linewidth laser (usually known as local oscillator) in the same spatial mode

and the emitted fluorescence appears at the beat frequency. The technique is very

sensitive as the beat frequency signal can be improved by increasing the local oscillator

intensity. But such heterodyne measurements require efficient single spatial

mode observation of fluorescence. For free-space atoms, the most commonly used

tool to collect fluorescence is usually a lens [22, 23, 25]. But the limitation of the

lens system is that it collects fluorescence in many modes and fluorescence intensity

in single spatial mode is very small. So those systems require large number of

atoms, to have considerable fluorescence intensity in one spatial mode. Moreover,

due to spherical aberrations associated with lens systems, it is difficult to develop a

high numerical aperture (NA) lens system with NA more than 0.3 (∼1-2 % collection

efficiency in multiple modes). The requirements become more stringent if the

fluorescence emission spectrum is distributed in a wide frequency range wider than

the natural linewidth of atoms. Many smart structures have been proposed, where

the fluorescence from atoms are coupled efficiently to a single spatial mode, for example

a high-finesse optical cavity, where fluorescence from a single atom have been

detected in a single spatial mode[26, 27, 28, 29]. Such cavity systems are high finesse

micro-cavities and realize strong coupling between atom and photons, due to cavity


1.3. Optical Nanofibers for LIF Spectroscopy 7

quantum electrodynamics (QED). But the technical challenges associated with such

experiments are quite large, like building the cavity itself and realization of high reflectivity

mirrors for greater finesse [30] etc.. Moreover, such fluorescence light needs

to be coupled into some waveguides for next stage use and hence some additional loss

of signals strength.

In this thesis, we discuss the use of ultrathin optical fibers, with diameters less

than the propagation mode wavelength of the fiber, known as optical nanofibers for

measurement of the LIF spectrum of atoms. Optical nanofibers are circular waveguide

structures with a core, which is usually made of silica and a surrounding vacuum

clad. The propagating field through the nanofiber is confined in space in the transverse

direction of the nanofiber, and the mode density of the electromagnetic field

is modified around the nanofiber. For a particular fluorescence wavelength, with a

proper choice of the nanofiber diameter, propagation of only the fundamental HE 11

mode can be maintained through the guided modes of the nanofiber [31, 32]. Also,

there is a large evanescent tail in the transverse plane of the propagating guided

modes of the nanofiber. The intensity gradient of this evanescent tail can be used to

generate optical dipole potential for trapping atoms around the nanofiber [33, 34]. For

an atom near the nanofiber, due to the modified mode distribution by the nanofiber

and confinement of the propagating guided-modes, a significant fraction of the atomic

emission can be channeled in the single-guided-modes of the nanofiber [35]. In the

next section, we discuss in details about the properties of optical nanofibers and their

advantages for fluorescence measurements even for a small number of atoms.

1.3 Optical Nanofibers for LIF Spectroscopy

Recently, ultrathin optical nanofibers with sub-wavelength diameters have attracted

considerable attention. Our group proposed a novel idea for realizing slow light

propagation in a thin optical fiber by utilizing the electromagnetically induced transparency

(EIT) properties of the surrounding medium [36]. The fabrication of such

optical nanofibers with diameters down to 50 nm and with very low transmission


Chapter 1. Introduction 8

loss has been demonstrated by Mazur’s group [37]. Russell’s group demonstrated

spectrally-broad single-mode supercontinuum generation using the unique property

of propagating field confinement in micron and submicron tapered fibers [38]. Also

due to the evanescent tail of the guided-modes, tapered optical fibers with micrometer

diameters have shown promising appication as efficient light couplers to high Q

micro-resonantors such as silica microspheres and microtoroids [39].

It has recently been demonstrated by our group that an appreciable amount of

fluorescence photons from a small number of atoms lying around the nanofiber can

be channeled in the guided-modes of the nanofiber [40]. Also, since atoms emitting

fluorescence in the guided-modes of the nanofiber lie very close to the nanofiber surface,

atom-surface interactions have been observed through the fluorescence excitation

spectrum measurements [40]. Moreover, it has been demonstrated by our group that

the surface conditions can be manipulated by the irradiation of MOT-atoms with the

UV laser [41, 42] and by manipulating the MOT experimental parameters [41]. Single

atoms on an optical nanofiber have been detected successfully and their photon

correlations were investigated theoretically and experimentally [42, 43, 44]. Such a

nanofiber technique has been used to probe cold atoms around the nanofiber using

absorption spectroscopy [45]. Recently, a two-color based optical dipole trap around

a nanofiber has been demonstrated [34, 46]. Non-linear optical processes have been

observed for hot vapor-atoms at very low probe power levels using nanofibers [47, 48].

Also, fluorescence emission spectrum of a layer of molecules adsorbed on the surface

of the nanofiber has been investigated using a commercial spectrum analyzer [49].

Till now, no work has been done to develop nanofiber as a tool to measure not only

the LIF excitation spectrum but also the LIF emission spectrum of a small number

of atoms with a high resolution. The purpose of the present work is to develop and

demonstrate a fluorescence measurement spectrometer using optical nanofibers for

measurement of the LIF excitation and the emission spectrum of a single or a small

number of atoms with a resolution better than the natural linewidth of the atoms.

In the next section we discuss in detail the properties of optical nanofibers for the

measurement of fluorescence spectrum.


1.3. Optical Nanofibers for LIF Spectroscopy 9

a)

Evanescent Region

Nanofiber Guided Field

Vacuum Clad

Silica Core

2a

Silica

Vacuum

n core

n clad

b) c)

Penetration Length [nm]

1500

1000

500

a=100nm a=200nm

0

0 500 1000 1500

Wavelength [nm]

a=300nm

a=400nm

Field Profile [a.u.]

1.0

0.8

0.6

0.4

0.2

I = 850 nm, a = 200 nm

I = 850 nm, a = 400 nm

0.0

0 1 2 3 4 5

r/a

Figure 1.2: (a) Schematic diagram showing the single mode propagation of field

through the guided mode of the nanofiber. These are vacuum clad fiber and a part of

the field exist outside the fiber, in the evanescent region. The parameters, n core and

n clad are the refractive indices of the core and clad respectively. (b) The dependence

of the penetration length on the wavelength of the propagating light field for different

fiber radius (a), from 100 nm to 400 nm. (c) The normalized field profile versus the

normalized radial distance (r/a) for 850 nm light propagating through the nanofiber

with radius 200 nm (black curve) and 400 nm (red curve).

1.3.1 Mode Structure in Optical Nanofibers

Optical nanofibers core is made up of silica and the clad is the surrounding vacuum

medium. The inner silica core refractive index (n core = 1.45) is much larger than

the outer vacuum clad (n clad = 1). This large difference between the refractive indices

(∼0.45) makes the nanofiber different from a conventional weakly guiding fibers where

the difference in the refractive indices of the core and the clad is around ∼0.005 [31].

The large difference in refractive indices and the thin thickness of the nanofiber mean

that the linearly polarized (LP) modes which are the approximate solutions of the


Chapter 1. Introduction 10

eigen-value equations for modes propagating through the weakly guiding fibers are no

longer valid and exact solutions of the Maxwells equations are needed to determine

the propagating modes. The exact solutions of the propagating modes of an optical

nanofiber subjected to boundary conditions imposed by the waveguide geometry have

been calculated [31]. The propagating modes inside the optical nanofiber (known

as the guided modes) are the HE modes and not the LP modes of weakly guiding

optical fibers. The nanofiber mode characteristics depend on the fiber radius a and

the propagating light wavelength λ. Due to the thin thickness of the fiber, with

diameter less than the propagating wavelength, only the fundamental HE 11 mode can

propagate inside the nanofiber [32]. The exact intensity distribution and polarization

orientations of the propagating field in optical nanofibers have been calculated [32].

Also it has been shown that such thin nanofibers have very high power density at

their surfaces and there is a cylindrical asymmetry in the field distribution [50]. Also,

due to the small diameter of the nanofiber, a part of the propagating guided mode

field lies outside the fiber, in the evanescent region of the fiber. The penetration

length of the evanescent wave of the propagating guided mode is very large [33]. In

the linear polarization approximation, the spatial dependence of the amplitude of the

field outside the fiber is desribed by the modified Bessel function K 0 (qr). Here the

parameter q =1/Λ is the inverse of the characteristic decay length Λ of the field in

the evanescent region and is determined by the fiber eigenvalue equation [31]. Figure

1.2(a) shows the schematic diagram of nanofiber guided mode with a part of the

field propagating outside the nanofiber. The field in the evanescent region decays

exponentially outside the nanofiber and the characteristic decay length Λ is called

the penetration length or the evanescent tail. Figure 1.2(b) shows the dependence of

penetration length on the wavelength for different fiber radius. For a given fiber radius

the penetration length increases with wavelength, where as for a given wavelength

the penetration length increases with decreasing fiber radius. Figure 1.2(c) shows the

field-profile distribution of 850 nm light guided through fiber with radius 200 nm and

400 nm. The figure shows that for a smaller radius not only the penetration length is

longer but also a major part of the intensity lies outside the fiber. This strong field in


1.3. Optical Nanofibers for LIF Spectroscopy 11

the evanescent region around the nanofiber can be very promising for trapping and

detecting atoms.

1.3.2 Modified Spontaneous Emission of Atoms Around the

Nanofiber

Fluorescence is an example of the spontaneous emission process. The fluorescence

emitter can be atom, molecule or an ion and is initially assumed to be in an excited

state. In the present work, the emitter is in the excited state due to laser induced

excitation. Spontaneous emission of a photon is a result of the transition made by

an emitter from an excited state to the ground state. The spontaneous decay of

the atom is a probabilistic quantum-mechanical process which is induced by vacuum

fluctuations. The important point is that spontaneous emission is not an atom’s

intrinsic process but is subject to external influence.

The probability of spontaneous emission is given by Fermi’s golden rule

Γ ij ∝|D ij | 2 ρ(ν ij ) (1.1)

where Γ ij is the rate for the transition between the excited state i and the lower-energy

state j, D ij is a matrix element that connects the excited and lower energy levels and

is determined by the wavefunctions asscociated with those levels, ρ(ν ij ) is the density

of the optical field at the transition frequency or the photon mode density. Now as

seen from the equation for the transition rate, spontaneous emission rate of an atom

can be modified either by changing the D ij -term or the ρ(ν ij ) -term. The presence

of an interface near the atom can modify both the terms. In case of modification of

D ij -term, the atom and the interface should be very close or nearest neighbours (in

the solid or liquid state). A typical value of that separation is the atom wavefunction,

approximately 1 Å. The modification of the photon mode density ρ(ν ij ) -term due

to the presence of the interface occurs for a separation of the wavelength of emission

(∼ sub-µm) and is hence more simple and realistic for experimental purposes. This


Chapter 1. Introduction 12

control of the fluorescence decay rate through photon mode density using a cavity

was first discussed by Purcell at microwave frequencies [51].

An optical cavity with an atom inside it is the best known example where the photon

mode density is modified due to multiple reflections from the cavity mirrors. The

same physics can be extended to any material body. For example an interface, where

an atom is placed near a planar body where the photons emitted by the atom can be

reflected by the panar surface depending on its material properties like conductivity

etc. and can re-excite the atom. Many sophisticated ways to modify the mode density

have been proposed like microcavtiy, photonic solids and waveguides. Especially in

case of cavity and waveguide structures, not only the photon mode density is modified

around those structures but also the mode distribution is strongly confined to the

cavity or waveguide modes. The reflected wave from this cavity/waveguide structures

can interfere with the atom constructively and can enhance the spontaneous emission

rate of the atom and due to the mode confinement to the waveguide modes, a significant

fraction of the spontaneous emission can be coupled to the cavity/waveguide

modes.

In the present work, the interface is the optical nanofiber. The mode density of

the electromagnetic field is modified by the nanofiber and there is a confinement of

the propagating guided modes. The presence of optical nanofibers at a distance of

wavelength of emission from an atom, modifies the spontaneous emission rate of the

atom and due to the confinement of the propagating guided modes, an appreciable

amount of fluorescence photons can be channeled into single guided modes of the

nanofiber [35].

A detailed theoretical investigation of modified spontaneous emission of Cs-atom

around a nanofiber can be found in Ref. [35]. The theory includes a realistic model

of multilevel structure of Cs-atoms around an optical nanofiber. The spontaneous

emission of the Cs D 2 line 6P 3/2 → 6S 1/2 transition at λ 0 = 852 nm is considered.

The atom is assumed to be excited to the hyperfine structure level F ′ = 5 of the state

6P 3/2 . Due to selection rule spontaneous emission from the hfs level 6P 3/2 F ′ = 5 to the

ground state is always to the hfs level 6S 1/2 F = 4. The transitions between various


1.3. Optical Nanofibers for LIF Spectroscopy 13

magnetic sublevels are considered, assuming fiber axis as the quantization axis. It

is assumed that the fiber has a cylindrical silica core of radius a and the refractive

indices of the fiber and the vacuum clad are n 1 =1.45 and n 2 = 1, respectively. The

electric component of the field around the nanofiber can be decomposed into the

contributions from the guided and radiation modes. The evanescent modes do not

contribute to the spontaneous emission process. The fields in the radiation and guided

modes are quantized using the continuum field quantization procedure. Assuming

the field to be initially in the vacuum state and using Markoff approximation, the

Heisenberg-Langevin equations are derived for the atomic operators which give the

general and analytical expressions for the decay terms. In order to find the decay rate

of the population of an arbitrary level, the decay rates of all the associated downward

transitions are summed up. Both diagonal and off-diagonal decay terms appear due to

the assumed multilevel structure of Cs-atom. The diagonal terms describe the decay

rate of a particular magnetic sublevel and off-diagonal terms describe the coherences.

We discuss here the diagonal elements regarding the decay terms.

Figure 1.3(a) shows the schematic diagram of an atom emitting around a nanofiber.

The emission field near the nanofiber consists of both guided modes and the radiation

modes. Figures 1.3(b), (c), and (d) show the spontaneous emission rates for varios

magnetic sublevels 6P 3/2 F ′ =5M ′ of Cs-atom into guided modes γ ee (g) , radiation modes

γ (r)

ee

and the total emission modes Γ ee = γ (g)

ee

+ γ (r)

ee , respectively as functions of the

position of the atom r, from the fiber surface. The fiber radius used is a= 200 nm.

The rates are normalized to free-space decay rate Γ 0 =33× 10 6 s −1 . The different

magnetic sublevels of the same state 6P 3/2 have different decay rates in the vicinity

of the fiber surface, unlike the case of atomic Cs in free space. Different lines in each

plot correspond to different values |M ′ | = 0, 1, 2, 3, 4, and 5. The figure shows that

the presence of the nanofiber near the atom modifies the spontaneous emission rate

of the atoms and produces substantial decay rates into the guided modes. When the

atom is positioned on the fiber surface the decay rates into guided modes vary from

0.31 Γ 0 for M e =0 to 0.48 Γ 0 for M e = ±5. The decay rates into radiation modes

and the total decay rates are enhanced from the free-space rate by small factors. The


Chapter 1. Introduction 14

(a)

(r)

γ ee

γ (g)

ee

Γ ee

γ

(g)

ee

= +

γ

(r)

ee

(b)

(c)

(d)

Figure 1.3: Modified spontaneous emission around the nanofiber. (a) Schematic

diagram showing an atom emitting around the nanofiber. The emission is coupled

to both guided and radiation modes. (b), (c) and (d) Spontaneous emission rates

for various magnetic sublevels 6P 3/2 F ′ =5M ′ of Cs-atom into guided modes γ ee (g) ,

radiation modes γ ee (r) , and both types of modes Γ ee = γ ee

(g) + γ ee (r) , respectively as

functions of the position of the atom. Different lines in each plot correspond to

different values |M ′ | = 0, 1, 2, 3, 4, and 5. The fiber radius is a =200 nm. The rates

are normalized to the free-space decay rate Γ 0 .


1.3. Optical Nanofibers for LIF Spectroscopy 15

Figure 1.4: Coupling of spontaneous emission into the guided modes. (a) Fractional

decay rates into the guided modes as a function of distance of atom from the nanofiber

surface for fiber radius a = 200 nm. (b) Fractional decay rates into guided modes as a

function of fiber size parameter k 0 a, where k 0 is the free space propagation constant,

assuming the atom to be on the surface of the fiber. Different lines in each plot

correspond to different magnetic sublevels 6P 3/2 F ′ =5M ′ .

peak values of γ (r)

ee /Γ 0 and Γ ee /Γ 0 are 1.2 and 1.6 respectively. The enhancement of

the decay rates is largest when the atom is on the fiber surface and as atom moves

away from the fiber surface the deacy rate into the guided modes γ ee

(g) reduces to zero

and γ ee

(r) and Γ ee approach the free-space value Γ 0 . The small oscillations around the

value of unity for γ ee (r) /Γ 0 are due to the constructive and destructive interferences of

photons reflected from the fiber surface.

The decay rate not only depends on the position of atom from the fiber surface

but also depends on the fiber size parameter k 0 a, where k 0 is the free space propagation

constant. The factional decay rates γ ee (g) /Γ ee for various magnetic sublevels have

been calculated by our group and are plotted in Fig. 1.4(a) and (b) as a function of

r/a and k 0 a respectively [35]. The fractional decay rate γ ee (g) /Γ ee gives the coupling

efficiency of spontaneous emission into the guided modes. Figure 1.4 shows the op-


Chapter 1. Introduction 16

timum conditions for coupling of atomic fluorescence into the guided modes. In Fig.

1.4(b) the atom is assumed to be on the fiber surface and the fractional decay rates

for various magnetic sublevels are plotted as a function of the fiber size parameter,

k 0 a. The plot shows that γ ee (g) /Γ ee varies with fiber size parameter and is maximum

at around k 0 a = 1.45, which is determined by the refractive index of the fiber n 1 =

1.45. For Cs-atom D 2 - transition wavelength of λ 0 = 852 nm, with k 0 =2π/λ 0 , the

optimum size parameter corresponds to fiber radius of a ∼ 200 nm. In Fig. 1.4(a)

the fractional decay rates are plotted as a function of position of atom from the fiber

assuming a fiber radius of a ∼ 200 nm, the optimum coupling condition. The fractional

decay rates into the guided modes are maximum for atoms lying close to the

fiber surface and with increasing distance from the fiber surface the coupling γ ee (g) /Γ ee

reduces to zero within around ∼5a. The optimal value for the fractional decay rates

can be in the range from 0.2 for M e =0 to 0.28 for M e = ±5.

So, the presence of nanofiber interface near the atom substantially affects the

spontaneous emission process. The spontaneous emission is enhanced in the vicinity

of the nanofiber and due to confinement of the field in the guided modes and the

degeneracy of the excited and ground states a significant fraction of the spontaneous

emission can be channeled into guided modes of the nanofiber. Different magnetic

sublevels have different decay rates and a coupling efficieny of up to 28 % for magnetic

sublevel M e =5 can be acheived in a realistic system of a Cs atom near a nanofiber.

Such high coupling efficiency of atomic fluorescence into the guided modes can be

promising for fluorescence investigation of small number of atoms.

Also another

important point about the nanofiber method is that it collects the fluorescence into

the single fundamental guided mode which enables single-mode observation of atom

fluorescence. This is important as conventional experiments involving fluorescence

measurement in free space use very high numerical aperture optics for fluorescence

detection and at best only a few percent of the atomic fluorescence is collected. The

coupling efficiency can be increased by increasing the solid angle of detection but then

the observation will no longer be a single mode observation and it will be a multimode

observation. In multimode observation the single mode characteristics are lost due


1.4. Optical Nanofibers as a Tool for Probing Atom-Surface Interactions 17

to averaging over a continuum of spatial modes. The preservation of the single mode

characteristics is important for the measurement of the fluorescence spectrum. Note

that the inclusion of the realistic hyperfine structure of the Cs-atom, in comparison

to a two-level atom [52, 53], for the calculation of the spontaneous emission decay

rate is important as it can affect the actual rate of spontaneous decay.

Regarding the measurement of the LIF emission spectrum, the fluorescence coupled

into the guided modes of the nanofiber needs to be dispersed in frequency domain.

We discuss two conventional high resolution measurement methods namely the optical

heterodyne technique (OHD) and the photon-counting based photon correlation

(PCR) spectroscopy for the measurement of the emission spectrum. We discuss the

limitations of these techniques regarding the measurement of the spectrum of a small

number of atoms. So for the spectrum measurement, we develop and demonstrate

a new sensitive and high resolution method consisting of OHD technique and PCR

spectroscopy. This method can be extended even to single atoms.

Furthermore, the fluorescence measurement based on optical nanofibers may become

a unique tool to probe atom-surface interactions. This is because atoms emitting

fluorescence into the guided-modes of the nanofiber lie very close to the nanofiber surface

and are subjected to atom-surface interactions. In the next section, we discuss

the use of optical nanofibers as a tool for probing atom-surface interactions.

1.4 Optical Nanofibers as a Tool for Probing Atom-

Surface Interactions

The study of atoms in the vicinity of a surface has revealed many interesting physics

associated with the atom-surface interactions and is still under active investigation

even after many years of research. Especially, a lot of investigations have been carried

out to understand the adsorption and desorption of alkali atoms from various

metal/dielectric surfaces [20, 21, 40, 54, 55, 56, 57, 58, 59, 60, 61]. Such studies

of atom-surface interaction are not only an important aspect of surface science re-


Chapter 1. Introduction 18

lated to variety of technological applications like coating and protection of metals,

colloidal chemistry, catalysis etc, but also for the understanding of outer space atmosphere

[56]. Moreover, in these days this subject has gained renewed interest due to

nanotechnology applications, near-surface cold atom physics and the various overlap

between quantum optics and solid-state physics [62, 63, 64].

The atoms approaching the surface may get stick (adsorption) or reflected (heating)

from the surface. The adsorption process may be understood as loading of

atoms into the surface potential to a depth of few meV (physisorption) to few eV

(chemisorption). Atoms getting physisorbed on to a surface stay there for a while

and then desorb away [21], where as chemisorbed atoms permanently stick to either

some regular surface sites or on some surface defect sites [55]. Desorption of

chemisorbed atoms from surface sites is also an important phenomenon, where the

adsorbed atoms may get desorbed from the surface due to direct electronic excitations,

photo-induced electronic excitations, thermal desorption or sputtering by an

impinging ion [54, 56, 58, 59]. The study of the dynamic process of surface coating

or the changing surface conditions due to adsorption and desorption of atoms may

reveal many interesting physics associated with the atom-surface interactions.

However, despite a great deal of research in this direction, certain aspects of such

atom-surface interactions are still not well understood. It is due to the lack of proper

experimental techniques to investigate the near-surface atoms and also because of

the challenges associated with controlling the surface conditions. Some of the usual

techniques in quantum optics to investigate the atom-surface interactions are selective

reflection spectroscopy [65], thin vapor cells spectroscopy [66] and micron-sized cavity

[67]. Due to the inherent nature of the nanofiber method only atoms very close

to the nanofiber surface, around 200 nm from the surface, can couple fluorescence

in the guided modes. At such small distances, atoms can experience atom-surface

interactions. Figure 1.5 shows the theoretical calculations of the surface-induced

potentials for a Cs atom near a semi-infinite silica medium [60]. The figure shows

the surface potentials for the ground and excited states 6S 1/2 and 6P 3/2 of Cs D 2

line transition respectively. It shows the atom-surface interaction potentials for a


1.4. Optical Nanofibers as a Tool for Probing Atom-Surface Interactions 19

Figure 1.5: Surface-induced potentials for ground and excited-state Cesium atoms.

The calculation have been performed for the D 2 -line transition of a Cs atom in the

vicinity of a semi-infinite silica medium.

separation of upto 2 nm from the fiber surface. The low-energy depth of the potential,

near the dissociation limit, extends upto ∼100 nm. So the nanofiber method can

be implemented to investigate the atom-surface interactions by observing the LIF

excitation and emission spectra through the guided modes.

In earlier experiments, the excitation spectrum measured for cold atoms using optical

nanofibers has shown signatures of atom-surface interactions [40]. The lineshape

of the excitation spectrum deviates significantly from that of the Lorentzian shape of

the free-space atoms and shows a large tail in the red-detuned side of the spectrum.

The lineshape of the excitation spectrum is understood as a result of the process

where atoms approaching the nanofiber surface fall into the local surface potential

forming long-range atom-surface bound states [20, 21, 60, 61, 40]. Also, it has been

reported that the excitation spectrum lineshape changes with time [40]. Recently, it

has been found that such surface interactions around the nanofiber can be modified by

the irradiation of the MOT-atoms with a 407 nm laser (UV laser) [42] and by manipulating

the MOT experimental conditions [41]. After such UV laser irradiation, the

lineshape of the excitation spectrum changes drastically and approaches Lorentzian

shape suggesting that the MOT-atoms are kept from falling into the surface-potential


Chapter 1. Introduction 20

and behave almost like free-atoms around the nanofiber. In this thesis, we systematically

investigate such changes in the lineshape of the excitation spectrum. In addition

to the excitation spectrum, we also investigate the fluorescence emission spectrum of

atoms. The details of the measurements are discussed in Chapter 4 of this thesis.

1.5 Chapter Overview

As described in the previous sections, optical nanofibers may become a promising tool

for measuring laser induced fluorescence spectra of atoms. In earlier experiments,

the LIF excitation spectrum of atoms have been measured using optical nanofibers

but the measurements of the LIF emission spectrum using nanofibers has not been

demonstrated yet. Both the LIF excitation and emission spectra measurements are

required to gain a complete understanding of the atomic fluorescence. Moreover,

in general there was no experimental evidence of the measurement of LIF emission

spectrum of a small number of atoms by any other methods (like high numerical

aperture optics), where the spectrum is distributed in a wide frequency range (wider

than the natural linewidth of atoms) and the measurement resolution is better than

the natural linewidth of atoms.

The purpose of the present work is to develop a fluorescence measurement tool

based on optical nanofibers for measuring both the LIF excitation and emission spectra

of strongly driven atoms. For the measurement of the emission spectrum, we

develop and demonstrate a new sensitive and high resolution method consisting of

optical heterodyne technique and photon correlation spectroscopy. As a first demonstration,

we have measured the LIF spectra of a small number of atoms. In the future,

the nanofiber method along with the heterodyne and correlation spectroscopy can be

extended for the fluorescence measurements of single atoms. Also since atoms, emitting

fluorescence in the guided-modes of the nanofiber, lie very close to the nanofiber

surface, the nanofiber method can be naturally extended to probe atom-surface interactions.

The present experimental work is based on the concept that the mode density


1.5. Chapter Overview 21

of electromagnetic field is modified by the nanofiber and there is a confinement of

the propagating guided-modes. The modified mode density distribution modifies the

spontaneous emission rate of the nearby atoms and the confinement of the guidedmodes

results in the channeling of a significant fraction of the atomic fluorescence

in the guided-modes. For the present experimental demonstrations, cold atoms are

prepared near a nanofiber using a magneto-optical trap (MOT) and the fluorescence

of atoms is detected through the guided-modes of the nanofiber.

Chapter 2 presents the experimental tools and techniques used in the present work.

First, we describe the techniques for nanofiber fabrication in our laboratory. Next, we

discuss the components used in the preparation of cold atoms in a magneto-optical

trap (MOT) - the vacuum system, the MOT trapping lasers and their frequency

stabilization, and the optics system. Next we discuss how to combine these cold

atoms with the nanofiber. The chapter then presents the excitation lasers, their

frequency stabilization techniques, the detection and the timing systems. Finally

the chapter concludes with the measurement of MOT characteristics like density and

temperature of the cold atoms.

Chapter 3 present the experiments for LIF excitation and emission spectra measurements

for strongly driven atoms. As reported in earlier experiments and mentioned

in Section 1.4, the UV laser irradiation of the MOT-atoms, kept the atoms

from falling into the surface-potential and the atoms behave almost like free-atoms

around the nanofiber. Under this free-atom conditions, we first carry out the spectra

measurements. The chapter first discusses the measurement of the LIF excitation

spectrum of atoms around the nanofiber. Then the chapter presents the precise measurements

of the number of atoms emitting fluorescence in the guided modes of the

nanofiber, based on photon-correlation spectroscopy. The experimental procedures

for the measurement of the LIF emission spectra are discussed followed by the observed

results. For the emission spectrum measurements, we discuss the conventional

high-resolution methods like OHD technique and PCR spectroscopy. We discuss their

limitations for measuring the LIF spectrum of a small number of atoms. We then

discuss a novel method which takes advantage of both the OHD technique and photon


Chapter 1. Introduction 22

counting based PCR spectroscopy. The theory of this combined method is discussed

along with the experimental procedures. The emission spectrum is investigated for

both on-resonant and off-resonant excitations.

Furthermore, as discussed in the last section, since atoms emitting fluorescence

in the guided-modes of the nanofiber lie very close to the nanofiber surface, they

are subjected to atom-surface interactions. So, fluorescence measurements based on

optical nanofibers may become a unique tool to probe atom-surface interactions.

In earlier experiments, the excitation spectrum measured using optical nanofibers

has shown signatures of atom-surface interactions. It has been reported that the

excitation spectrum lineshape changes with time. Recently, it has been found that

such surface-interactions around the nanofiber can be modified with the application

of a 407 nm laser (UV laser) and by manipulating the MOT experimental conditions.

In this thesis, we systematically investigate such changes in the lineshape of the

excitation spectrum. Chapter 4 presents both the LIF excitation and emission spectra

measurements for near-surface atoms and discusses various mechanisms involved in

changing the surface conditions.

Chapter 5 discusses the conclusions. The chapter also presents a future extension

of the present work, where we hope to create optical dipole traps around the nanofibers

by introducing trap laser lights through the guided-modes and perform fluorescence

measurements of these trapped atoms.


chapter 2

EXPERIMENTAL TECHNIQUES

Experimentally, the optical nanofiber (nanofiber) is realized by using tapered optical

fiber technology and the atoms under investigation are prepared in a magneto-optical

trap (MOT). We use laser cooled Cesium (Cs) atoms for the experiments for two

reasons. First, the observation region around the nanofiber is very small compared to

the wavelength and hence atoms at room temperature will quickly transit across the

nanofiber, quicker than the spontaneous emission time of the atoms. The atoms need

to be cooled down sufficiently so that they spend enough time near the nanofiber to

couple their fluorescence in the guided-modes of the nanofiber. And second by using

laser cooled atoms the transit-time broadening can be reduced, a pre-requisite for

high-resolution LIF spectroscopy. The MOT atoms are overlapped with the nanofiber

and the fluorescence photons coupled in the guided-modes of the nanofiber are then

detected at the ends of the nanofiber. So for the experiments tapered optical fiber

technology is combined with the laser cooling technology.

24


2.1. Experimental Realization of Nanofiber: Tapered Optical Fiber Technology 25

2.1 Experimental Realization of Nanofiber: Tapered

Optical Fiber Technology

The optical nanofiber is prepared by tapered-fiber technology. The essential point is

to adiabatically heat and pull a standard single-mode optical fiber in a controlled way.

This results in a tapered optical fiber where the thinnest part, which lies at the waist

of the tapered fiber, is the nanofiber. To achieve this purpose, various heating and

pulling systems are being used but the underlying principles are more or less identical.

The heating system should be able to achieve around 1700 ◦ C, which is required for

silica-glass optical fiber processing. Some of the examples of the heating system are

gas flame heating (usually Hydrogen/Oxygen) [37], CO 2 laser heating [68, 69] or a

CO 2 laser heated sapphire crystal microfurnace [70]. Every technique has its merits

and limitations. The gas flame heating has been used to realize tapered fibers but

requirements, like very precise control of gas flow to control temperature and high

purity of gas to avoid any unwanted deposition of contaminants on the fiber surface

make it technically very challenging. Also, the external environmental conditions

like air-currents etc. can affect the production reproducibilty of the nanofiber. The

CO 2 laser heating technique is comparatively cleaner but the fact that the amount

of energy absorbed by the fiber reduces with decrease in fiber thickness, puts a limit

on the minimum achievable diameter. The heating of the fiber by a CO 2 laser heated

microfurnace removes these limitations and proved to be the best way to realize

nanofiber. Also, recently an electric furnace consisting of an electric strip heater has

been used for producing tapered fibers with diameters down to 650 nm [71].

In the present work, we realize nanofiber using a microfurnace technique which

consists of a resistively heated ceramic heater [72, 73, 40]. The ceramic microheater

has high melting point for use in air and can endure a temperature of 2000 ◦ C. It

has a long life time and it provides a stable heating region. We use a commercially

available optical fiber coupler manufacturing machine (NTT-AT, Model FCI-7011)

for fabrication of the nanofiber as shown in Fig. 2.1. The fiber coupler production

machine consists of two major systems. First, the main unit consists of the fiber-


Chapter 2. Experimental Techniques 26

clamp, fiber-pulling unit, the micro-heater holder, the ceramic heater, non-contact

infrared thermometer, and the fiber-holding jig. The second system is the control

unit which consists of the controller, personal computer (PC), digital multimeter,

the ceramic heater power source with feedback control and a two port optical power

detector with FC connector. The temperature of heater and the speed of pulling can

be precisely controlled using the PC based controller. The temperature of the heater

is measured by the infrared detector and is controlled by the feedback control of the

heater source. The machine is primarily meant for fabricating fiber couplers but we

have optimized the pulling parameters namely the temperature of the heater, the

pulling speed of the fiber-holder, and the time duration of pulling, for our nanofiber

fabrication purposes.

Figure 2.1(a), shows the nanofiber fabrication system. The entire system is installed

inside a clean booth equipped with a HEPA (high-efficiency particulate air)

filter based air cleaner (Airtech, SS-MAC). The filter is located on top of the booth.

The air-cleaner continuously flow dust-free air from the top and keeps the fabrication

area clean. The speed of the airflow is controllable and a cleanliness of class 100

can be achieved with this kind of HEPA filter. The cleanliness is very important

because dust deposited on the nanofiber can create local scattering centers for the

evanescent field lying outside the nanofiber and hence can induce major transmission

losses. Figure 2.1(b) shows the detailed photograph of the main unit. The ceramic

heater, the fiber holder system, and the clamps. A schematic diagram of the ceramic

heater is shown in Fig. 2.1(c) [73]. The heat source is covered with an insulation to

get high and stable temperatures. The fiber damage caused by the vapor of the heat

source is prevented by the inner protective sealed core tube. The heater has a longitudinal

hole of diameter 2 mm at its center. It also has a longitudinal slit through

which to insert the fibers into the hole. The temperature was measured through the

slit. The fiber in the hole are heated homogeneously by the surrounding heat element.

The heater is user replaceable. Figure 2.1(d) shows various tools for nanofiber

preparation. Some of the important tools frequently used in the nanofiber fabrication

stages as well as in experiments are fiber stripper (125 µm precision), fiber-end cutter


2.1. Experimental Realization of Nanofiber: Tapered Optical Fiber Technology 27

(a)

PC

Clean Room

Control Unit

Main Unit

Precision End

Cutter

(b)

Photo-

Detector

Ceramic Heater

Clamps

Fiber Holder Nanofiber

Ceramic Heating

Element

Optical

Fiber

Heat Insulator

Electrical

Lead

Protective Core Tube

(c) Ceramic Micro-Heater

Fiber Connector

Tip Cleaner

Fiber &

Bobbin

Fiber Stripper

Fiber Stripper End Cutter

(d)

Figure 2.1: Nanofiber preparation. (a) Photograph of the nanofiber fabrication system

inside the clean room . It consists of the main and the control unit. (b) Photograph

showing the main unit in details. The ceramic heater, the fiber holder, fiber

clamps, and the photo-detector for measuring transmission. The nanofiber is difficult

to see but its ends can be seen in the photograph which are fixed to the fiber holder

using glass preforms. (c) A schematic diagram of the ceramic microheater. (d) Some

tools used for nanofiber fabrication and for the present experiments.


Chapter 2. Experimental Techniques 28

(Furukawa), optical connector-end cleaner (NTT-AT, ATC-RE-02) and fiber splicing

machine (Furukawa Splicer, Fusion based).

The nanofiber is prepared from standard single mode optical fibers (Fujikura, SM

10/125) available commercially in the market [40]. These fibers are bare fibers that

is without the outer mechanical jacket, which surrounds the inner acrylate polymer

coating. The bare single-mode fiber diameter is around 250 µm. We strip the outer

acrylate coating (which surrounds the cladding) chemically with acetone. The chemical

stripping is better than the mechanical stripping because of the low probability of

making any scratches on the fiber. The fiber diameter after stripping is 125 µm. The

core diamter is around 9 µm for a cutoff wavelength of 1.3 µm. The stripped fiber

is then fixed on the pulling unit, using the fiber clamps. The nanofiber fabrication

is carried out in two heat and pull stages to maintain adiabatic tapering condition.

In the first stage the fiber diameter is reduced from 125 µm to several µm and in

the second stage the diameter reduces to sub-µm, and is less than the propagating

wavelength. The final diameter can be tuned by a proper set of heating and pulling

parameters. During the fabrication process, the transmission of the fiber is monitored

continuously by sending light at 852 nm through the fiber and detecting it with the

optical detectors. The nanofiber is located at the waist of the tapered fiber. In this

region of the tapered fiber, the core is almost vanishing and the clad of the original

fiber is now the core of the fiber with the surrounding vacuum now serving as the

clad of the fiber. The reproducibility of the process is studied statistically.

Adiabatic tapering is crucial for maintaining single-mode propagation through the

tapered region and also for realizing minimum loss. The condition for single-mode

propagation is given by the parameter V (= (2πa/λ) √ n 2 core − n 2 clad

), which determines

how many confined modes can be supported by the step index optical fiber. The parameter

a is the radius of the fiber, λ is the wavelength under investigation, n core and

n clad are the refractive indices of core and clad of the step index fiber respectively

[32]. The thinnest region of the tapered fiber that is the waist of the tapered fiber, depending

on the diameter of the fiber and the propagating-wavelength, supports only

the fundamental mode.

However the tapered region, that is the transition region


2.1. Experimental Realization of Nanofiber: Tapered Optical Fiber Technology 29

(a)

(b)

c)

2 mm

4 cm

125µm

Tapered Optical

Fiber

d)

Nanofiber

SEM IMAGE

Diameter = 400 nm

Figure 2.2: Characteristics of nanofibers fabricated in our laboratory for the present

experiments. (a) Transmission measured for different diameters of the nanofibers,

using 852 nm light. (b) Diameter variation along the length of the tapered fiber. The

nanofiber is the minimum diameter region of the tapered fiber. The different curves

correspond to different nanofiber samples, which shows the statistical reproducibility

of our nanofiber fabrication process. All the nanofibers are prepared under the same

production conditions. (c) Schematic diagram of the tapered fiber showing the length

of the nanofiber and the tapered region. (d) A typical SEM image of a nanofiber,

with a diameter of 400 nm.


Chapter 2. Experimental Techniques 30

from the normal single-mode fiber diameter (fundamental core-mode) to the thinnest

part of the fiber (fundamental clad-mode), can support multiple-modes because of the

propagating modes inability to change its field distribution rapidly enough to keep up

with the variation of the fundamental local mode whose shape is determined by the

local taper diameter. There can be a loss of power from the fundamental propagating

mode to other higher-order cladding-modes. These loses can be minimized by adiabatic

tapering of the fiber to the thinnest part. The adiabatic tapering ensures that

the transition of fundamental core-mode to fundamental clad-mode takes place without

any loss of power to higher order clad-modes. This is important beacuse it is the

clad-mode which propagates finally through the thinnest part that is our nanofiber.

Usually, such adiabaticity is confirmed by measuring the taper angle at each and

every point of the tapering region. The taper angle can be defined by the ratio dr/dz

where z is the distance along the taper and r = r(z) is the local core radius. The

adiabatic tapering condition is then given by dr/dz ≤ (r/2π)[β 1 (z) − β 2 (z)], where

β 1 (z) and β 2 (z) are the local propagation constants for the fundamental mode and

the next higher order modes respectively [69, 74, 75, 76].

The diameter of the nanofiber (the thinnest part of the tapered fiber), the profile

of the tapered fiber diameter and the tapering length on each side of the nanofiber

are measured using a scanning electron microscope (SEM), with a resolution of 30

nm. After preparing the nanofiber, it is collected and fixed on a metal plate using UV

adhesives. The plate is then brought to a scanning electron microscope (SEM) for observations.

With the present technique, nanofibers with diameter down to 200 nm can

be fabricated. Figure 2.2(a) shows the measured transmission of the nanofiber with

respect to the minimum diameter of the tapered fiber. The transmission decreases

drastically, if the diameter of the nanofiber decreases below ∼400 nm. The loss of

transmission is due to coupling of propagating guided modes to radiation modes. For

the present experiments, we use the optimum nanofiber diameter of 400 nm, for efficient

coupling of fluorescence of Cs-D 2 transitions. For nanofibers of diameter 400

nm, the transmission achieved is ∼90 %. Figure 2.2(b) shows some of the nanofiber

samples of diameter ∼400 nm, prepared under the same heat and pull conditions.


2.2. The Magneto-Optical Trap (MOT) System 31

The results are quite reproducible and the minimum diameter is reproduced within

an error of ±10 %. The minimum diameter is almost uniform for 2 mm and is enough

for our experiments as the MOT atom cloud size is around 1 mm. The tapering

length is 4 cm on either side and long enough to satisfy the adiabatic tapering condition

as shown schematically in Fig. 2.2(c). Figure 2.2(d) shows the SEM image of

the nanofiber region. The figure shows a nanofiber with a diameter of 400 nm. The

transmission of the nanofibers just after preparation is around 90-95 %.

2.2 The Magneto-Optical Trap (MOT) System

For realizing longer staying times of atom in the observation region of the nanofiber,

we cool down the atoms using a magneto-optical trap (MOT) [77, 78, 79]. The MOT

system consists of ultra-high vacuum chamber, the cooling and repump lasers which

are frequency stabilized to the respective Cs-D 2 transitions, the optics systems and

the magnetic-field system.

2.2.1 The Vacuum System

A vacuum system is the assembly of the components used to obtain, to measure

and to maintain the vacuum in a chamber. The high-vacuum is needed to reduce the

collisions between the trapped Cs-atoms and the background atoms (Cs-atoms as well

as any other particle). Figure 2.3 shows the high vacuum system which consists of a

specially designed steel chamber for holding the nanofiber structure, pumps, guages

and pipes connecting them together. The system also consists of valves and electric

feedthroughs.

To achieve high vacuum conditions, three pumps are used to pump down the

vessel from atmospheric pressure to the ultra-high vacuum-pressure. The chamber is

first evacuated with the help of a rotary vane pump (Pfeiffer Vacuum) till we reach a

pressure of around 10 −2 − 10 −3 mbar. The pressure is measured with a compact cold

cathode guage (Pfeiffer Vacuum). At this pressure, the turbo-drag pump (Pfeiffer

Vacuum, model-TMU-071P) is started. After the pressure has reached 10 −8 mbar,


Chapter 2. Experimental Techniques 32

Ion

Pump

Gate

Valve

Expt.

Chamber

NF Port

Pressure

Guage

Rotary

Pump

Angle

Valve

Argon

Supply

Turbo

Pump

Figure 2.3: Photograph of the vacuum system for the MOT. The system shows the

various pumps, the pipes connecting them along with the gate and angle valves.

Also shown are the presuure measuring guage, the Ar gas inlet system, and the

experimental chamber.


2.2. The Magneto-Optical Trap (MOT) System 33

finally the sputter-ion pump (Ulvac Inc.) is switched on. All the three pumps are run

simultaneously for around 1-2 days, during which baking of the Cs-atom dispenser

(Cs-atom source in the vacuum chamber) is carried out, then we seal the chamber

from the turbo/rotary pump system with an angle gate valve. The turbo/rotary

system is switched off- and the system runs only on ion-pump system. The angle

valve can withstand high pressure difference, and in our system it can withstand a

pressure difference between atmosphere and a pressure of 10 −10 mbar. The ion pump

is noise-free, vibration-free and can run for months without requiring any kind of

maintenance. For a bake out system, we get around 10 −9 mbar in our system. We

routinely achieve a pressure of 10 −9 mbar in our chamber, even without extensive

baking and for frequent nanofiber installations.

2.2.2 The MOT Laser Systems: Distributed Feedback (DFB)

Lasers

For the MOT system, we use the Cs-atom closed-cycle D 2 - transition between the

6 2 S 1/2 F = 4 and the 6 2 P 3/2 F ′ = 5 states to cool and trap the atoms. The atoms

which are lost due to the occasional transitions to the 6 2 S 1/2 F=3 hyperfine groundstate

are recycled back to the 6 2 S 1/2 F = 4 ground-state by a repump laser beam

between 6 2 S 1/2 F =3to6 2 P 3/2 F ′ = 3 transitions.

We use distributed feedback lasers (DFB) for our MOT cooling and repump lasers

beacuse of the high power availability (∼150 mW) and easily achievable single-mode

conditions. The single-mode emission is enforced by a Bragg grating integrated into

the active section of the semiconductor material of the laser chip, defining the emitting

wavelength. Wavelength tuning is realized by altering the refractive index of

the semiconductor, which can be achieved by either changing the temperature or

the operating current. Recently, DFB laser chips have become available at various

wavelengths near the D 1 - and D 2 -line of alkali atoms.


Chapter 2. Experimental Techniques 34

The LD Chip

Collimating

Lens

Allignment

Rods

Cylindrical Lens Pair

Enclosing Box to Prevent

External Air Currents & Disturbances

Figure 2.4: Photograph of the DFB laser system. The LD-chip is mounted on a

commercial collimator system. Also shown are the collimating lens and the cylindrical

lens pair system. The total unit is placed inside an acryl-enclosure to prevent any

fluctuating air-currents. Also shown in the inset is a typical DFB laser beam profile

measured at a distance of 1 m from the LD. The beam diameter (at 13.5 % level) is

2 mm.

DFB Lasers Characterization

The DFB laser diode (LD) chip used for MOT cooling and repump beams is from

Eagleyard Gmbh. (EYP-DFB-0852-T0C03). The laser after collimation and proper

beam shaping, emits a power of 140 mW at a current of 180 mA in single spectral

(longitudinal) and single spatial (transverse) mode condition in our required wavelength

range. The diodes were mounted into a TO-3 style package with integrated

thermistor and thermoelectric coolers. A commercial low noise current driver (Thorlabs

LDC 202) with maximum current output of 200 mA has been used. It has an

external modulation control input (± 20 mA/V), for modulating the injection current

into the diode for feedback purposes. The temperature controller (Thorlabs TED

200) stabilizes the temperature of the diode chip quickly, within a few minutes. This

is because the temperature sensor and the thermoelectric element (TEC), both are

integrated within the diode chip.

The diode emission polarization is transverse electric (TE) in parallel plane. Figure

2.4 shows the setup for the DFB laser diode. The laser diode chip is mounted

on a commercial mount having an integrated collimater flange (for holding the col-


2.2. The Magneto-Optical Trap (MOT) System 35

(a)

(b)

(c)

Wavelength (nm)

Wavelength (nm)

852.4

852.2

852.0

851.8

851.6

851.4

852.20

852.15

852.10

852.05

852.00

Power (mW)

160

140

120

100

80

60

40

20

Injection current (167mA)

Wavelength (nm)

Frequency (GHz)

20 22 24 26 28 30 32 34 36 38

Temperature ( 0 C)

Temperature 32 o C

Wavelength (nm)

Frequency (GHz)

100 120 140 160 180 200

Current (mA)

With ND13 filter

Callibrated

0

20 40 60 80 100 120 140 160 180 200

Current (mA)

352000

351950

351900

351850

351800

351750

351700

351650

351600

Frequency (GHz)

351790

351780

351770

351760

351750

351740

351730

351720

351710

351700

Fequency (GHz)

Figure 2.5: Characteristics of cooling DFB laser. (a) Dependence of wavelength

on temperature. The frequency variation is also shown. The LD injection current

has been kept fixed at 167 mA. (b) Dependence of wavelength on Current for a

temperature of 32 ◦ C. (c) Power - current characteristics measured with a callibrated

power meter and neutral density (ND) filters.


Chapter 2. Experimental Techniques 36

limating lens) and an anamorphic beam shaping optics (Schafter & Kirchoff). The

collimation lens is an anti-reflection coated aspheric lens of focal length 4.5 mm (NA

0.55) and the collimated elliptical beam is then converted into a circular beam by

the anamorphic cylindrical lens pair system. The lens pair system has some advantages

over conventional anamorphic prism pair system. It removes the astigmatism

associated with the beam and there is a negligible power loss across it . The output

power available after the cylindrical lens system is ∼140 mW at 180 mA. The DFB

lasers are very much prone to back reflections into the diode chip which can make

it very unstable. So, it is essential to isolate the diode chip from back reflections.

This is also important since the trapping lasers will be used as MOT trapping beams,

where 180 0 retroreflected beams will be used. An optical isolator (Isowave) with 40

dB isolation and 0.7 dB insertion loss is used for this purpose and the power at the

isolator output is around 120 mW. The beam profile measured with a CCD camera is

shown in the inset of Fig. 2.4. It shows a single transverse-mode profile. The characterization

of the diode laser have been carried out with an optical spectrum analyzer

(OSA) (TechnoOptics - Febry-Perot cavity and detector, CVI optics -the piezodriver

and amplifier) and a wavemeter (Burleigh- WA1500). The OSA free spectral range

(FSR) is 2 GHz and finesse is 200 which gives a cavity linewidth of 10 MHz sufficient

for diagnosing the single mode conditions of the laser. The wavemeter has a

frequency resolution of 0.0001 nm (∼ 40 MHz) for a input laser linewidth of less than

1 GHz. It measures the wavelength using the principle of Michelson interferometer

using a stabilized He-Ne laser at 632 nm. The DFB laser diode, in the wavelength

range for present experiments, emits always in the fundamental single-mode. It has

a mode-hop-free spectral range of more than 1 nm (∼ 400 GHz).

The tuning range of the laser was determined with the wavelength meter. The

output frequency can be tuned by varying either the temperature of the chip housing

or the operating current of the diode. With temperature, the resonance wavelength of

the integrated grating changes by approximately 0.06 nm /K, while the gain spectrum

varies at a rate of ∼ 0.2 nm /K. Thus, the resonant wavelength shifts to the side of the

gain spectrum, which eventually limits the accessible wavelength range of the DFB


2.2. The Magneto-Optical Trap (MOT) System 37

(a)

(b)

(c)

Wavelength (nm)

Wavelength [nm]

852.18

852.17

852.16

852.15

852.14

852.13

852.12

852.11

Power [mW]

852.15

852.10

852.05

852.00

851.95

851.90

80

70

60

50

40

30

20

10

Injection current = 126 mA

Wavelength (nm)

Frequency (GHz)

12.8 13.0 13.2 13.4 13.6 13.8 14.0

Temperture ( o C)

Temperature = 10 o C

40 60 80 100 120 140

Current [mA]

40 60 80 100 120 140

Current [mA]

351734

351730

351726

351722

351718

351714

351710

351706

Frequency (GHz)

Figure 2.6: Characteristics of repump DFB laser. (a) Dependence of wavelength

on temparature. The frequency variation is also shown. The LD injection current

has been kept fixed at 126 mA. (b) Dependence of wavelength on Current for a

temperature of 10 ◦ C. Such a low temperature has been used to tune the wavelength

near to the MOT repump transition. (c) Measured power-current characteristics.


Chapter 2. Experimental Techniques 38

diode [80]. The thermal tuning rate characteristics for the DFB laser at a current

of 167 mA (current at which the laser is locked as discussed in later sections) to be

used as a cooling laser for MOT is plotted in Fig. 2.5(a). The diode temperature

was increased from 20 ◦ C to 38 ◦ C while the emission wavelength was monitored

with the wavelength meter. The wavelength varied between 851.5 nm and 852.4

nm, with no mode-hopping. Single-mode emission was maintained over a wavelength

range of more than 1 nm (400 GHz). The data yield an average thermal tuning rate

of △ν / △T = - 28 GHz / K (+ 0.07 nm / K). Figure 2.5(b) shows the current

tuning rate characteristics. The modulation of the current changes both the carrier

density and the internal temperature of the semiconductor chip. The thermal effect is

comparably slow and becomes less relevant with increasing tuning rates. The tuning

rate (MHz/mA) amounts to ∼930 MHz /mA at slow modulation frequencies (∼1

mHz) and it decreases to 370 MHz /mA at higher modulation frequencies (∼10 Hz).

The temperature and current have been adjusted in such a way that the power of the

diode laser measured after the anamorphic beam shaping optics shows a maximum

at the operating wavelength of 852.13 nm, that is the cooling transition. Figure

2.5(c) shows the power-current characteristics of the diode just after collimation. A

high sensitive wavelength adjustable power meter (Advantest, maximum power- 50

mW) has been used for the measurement. Properly callibrated neutral density (ND)

filters have used for measurement of powers exceeding 50 mW. It has mode-hop free

operation in our working wavelength range and it always emits in the fundamental

spatial (transverse) single-mode, the TEM 00 mode.

The characteristics for the DFB laser to be used as a repump laser for MOT are

plotted in Fig. 2.6. The thermal and current tuning characteristics are same as for

cooling laser. The working power is 70 mW.

2.2.3 Laser Stabilization and Frequency Control

The cooling and repump beams for the MOT are stabilized to suitable Cs D 2 -lines.

The optical transitions of the Cs D 2 -line to which the cooling and repump beams are

locked, are shown in Fig. 2.7. The standard frequency modulation (FM) technique


2.2. The Magneto-Optical Trap (MOT) System 39

combined with the saturated absorption spectroscopy (SAS) has been used for locking

the lasers [81, 82, 83]. The FM technique has been used to derive the frequency

dependent error signal from the saturated absorption signal. Figure 2.8 shows the

schematic diagram of the experimental setup used for cooling- and repump- laser

locking to the atomic line. The essential point of SAS is the use of two counterpropagating

beams, a weak probe beam and a strong pump beam through a Cs-vapor

glass cell and detecting the absorption signal (SAS signal) of the probe beam. The

probe beam is scanned across the D 2 -transition. The probe absorption signal without

the pump beam for the thermal atoms of the vapor cell is a Doppler broadened

spectrum as shown in Fig. 2.9(a). In presence of pump beam, the SAS technique

produces sub-Doppler spectral lines, which can be used to stabilize the laser. The

probe absorption is minimum at the atomic transition frequency due to saturation

by the strong pump beam. This results in a saturation peak in the absorption signal.

Along with the atomic resonances, there will be crossover peaks at frequencies which

lie at the center of two resonances as shown in Fig. 2.9(b). The atomic resonances

along with the cross-over resonances can be seen in the figure. The lasers are locked

to the peak of the suitable atomic transitions. The frequency location of the peak

of the transition is relatively insensitive to intensity and broadening effects, which

would otherwise change the locking set point if the lasers were locked instead to the

side of the line. The next step is to generate error signal for locking purposes which

is the derivative of the SAS signal.

First, we discuss the locking of the cooling laser to the Cs-atom D 2 -transition

F=4→ F’=5. Figure 2.8 shows the experimental setup. The cooling DFB laser

output is splitted into two beams with different power ratios (1 : 3). The weak one

is used as the probe beam and the stronger one as the pump beam. The probe beam

power for SAS is ∼ 130 µW and the pump power is ∼ 350 µW. A commercial resonant

electromagnetic modulator (EOM) has been used to frequency modulate the probe

beam. The collimated probe beam is focussed onto the EOM with a lens (f =10

cm). Finally the modulated probe beam distorted by the spectral features of the SAS

is collected by a low noise photodetector (Newfocus 1811AC, DC-125 MHz). The


Chapter 2. Experimental Techniques 40

'

F =5

251 MHz

+113 MHz

201 MHz

151 MHz

+75.6 MHz

'

F =4

'

F =3

'

F =2

6 P3/2

9.2 GHz

Cooling

Transition

Repump

Transition

F=4

F=3

6 S1/2

Figure 2.7: The Cesium D 2 transitions to which the MOT cooling and repump lasers

are locked. Also shown are the frequency upshifting by the AOM’s used for creating

the MOT.

Feedback

Circuit

LD

Driver

Current Feedback

DBM

PD

M

HM

Probe

10cm

Phase

Shifter

Pump

Cs Cell

Function

Generator

RF Signal

EOM

10cm

PBS

M

λ/2

Isolator

Cyl. Lens

Pair

Temperature

Controller

DFB

Laser setup

Figure 2.8: DFB laser locking system. The same configuration has been used for

locking both the cooling and the repump lasers. It shows the optical setup for the

saturation absorption spectroscopy with frequency modulation by EOM. It also shows

the main electrical components used for the locking.


2.2. The Magneto-Optical Trap (MOT) System 41

Voltage (v)

(a)

0.28 Doppler broadened profile

0.24

500 MHz

0.20

0.24

0.20

0.16

(b)

F = 4 -> CO [ F' = 2,4 ]

F = 4 -> CO [F' = 3,4 ]

F = 4 -> CO [ F' = 3,5 ]

F = 4 ->

CO [ F' = 4,5 ]

F = 4 -> F' =4

F = 4 ->

F'= 5

0.16

-0.03 -0.02 -0.01 0.00 0.01

Time (s)

line (852.13 nm)

0.12

Cs D 2

-600 -400 -200 0 200 400 600

Frequency (MHz)

Figure 2.9: The cooling DFB laser SAS characteristics. (a) The absorption of the

probe signal when no pump beam has been used. The laser is scanned across the

atomic resonances. The Doppler broadened signal with FWHM of ∼ 500 MHz can

be seen. The small peaks seen in the Doppler broadened profile is due to reflection

of probe beam from the uncoated (no AR-coating) cell wall. (b) same as (a) but the

pump is now on. The various sub-Doppler resonances and cross-over (CO) resonances

can be seen in the signal.

detector has a built-in preamplifier which helps in increasing the signal to noise ratio

(SNR). For efficent collection, a lens has been used (f =10 cm) to focus the probe

beam on to the detector. As mentioned before, Fig. 2.9 shows the Doppler broadened

profile (with no pump beam used) and the SAS signal observed at the ouput of the

detector. For locking to the atomic line, we frequency modulate the probe beam

using an electro-optic modulator (EOM) at 11.72 MHz. The photodetector detects

the frequency modulated SAS signal. The detector output is fed to RF input of a

double balanced mixer (DBM, Minicircuits frequency mixer chip TUF 3+, DC- 400

MHz). A standard wavefunction generator (wavefactory 1946 B) has been used for

driving the EOM and it also provides the sync signal for the local oscillator (LO)

of the DBM. An impedance matching voltage divider circuit has been used to keep

the LO input levels within the specified range. The DBM mixes the detector output

with the LO signal to derive the differentiated absorption line which is used as the

error signal for locking the laser to the atomic line. The output of the DBM also

depends on the phase difference between the two input signals. The phase mismatch


Chapter 2. Experimental Techniques 42

Voltage [V]

0.28

0.24

0.20

0.16

0.1

0.0

-0.1

-0.2

F = 4 -> CO [ F' = 4,5 ]

-0.020 -0.015 -0.010 -0.005 0.000 0.005

Time (s)

SAS signal

Error signal

Figure 2.10: The error signal (lower grey curve) of the cooling-DFB-laser observed

at the monitor ouput of the locking circuit. For comparison the corresponding SAS

signal is also shown (upper black curve) in the plot. The dashed line shows the

cross-over transition (CO) to which the laser is locked.

between the EOM sidebands and the LO is compensated by a commercial voltage

controlled phase shifter (Minicircuit, JSPHS-12, 0-180 0 ) to control the shape and

sign of the error signal. The error signal generated at the output of the mixer is fed

to a feedback circuit. The feedback circuit is a home-built one and consists of two

main components- A variable gain buffer for error signal monitoring purposes and

a low pass filter based current-feedback circuit. We discuss in details the feedback

circuit in the next paragraph. A typical error signal (gray curve) observed at the

output of the monitor circuit is shown in Fig 2.10. It shows all possible hyperfine

resonances along with the crossover resonances for transition from 6S 1/2 F = 4 ground

state hyperfine level. We use the last crossover transition for locking the laser, as it

crosses zero almost at the center and is symmetric. The offset for other resonances

is due to the Doppler profile. For comparison, the corresponding SAS signal (black

curve) has also been plotted in the figure.

To realize a reliable locking system, the detection system should be as much

noise-free as possible. It is important that the RF-oscillator producing the modu-


2.2. The Magneto-Optical Trap (MOT) System 43

Frequency (MHz)

10

5

0

-5

SAS signal

Locked signal

-10

0.0 0.01 0.02 0.03 0.04

Time (s)

Figure 2.11: The error signal of the cooling DFB laser under locked condition (gray

curve). The SAS signal (black curve) is also shown for linewidth comparisions.

Voltage [V]

0.2

0.1

0.0

-0.1

(a)

Unlocked error signal

Locked error signal

-0.2

0 20 40 60 80 100

Time (s)

No. of Occurances [a.u.]

500

400

300

200

100

0

(b)

FWHM= 1.75MHz

-3 -2 -1 0 1 2 3 4

Frequency [MHz]

Figure 2.12: (a) The cooling laser error signal for free running (black curve) and

locked condition (grey curve). The laser is placed at the cross-over resonance. (b)

The laser linewidth estimation, using standard deviation method for laser frequency

variations, comes out to be around 1.7 MHz.


Chapter 2. Experimental Techniques 44

lation frequency be as stable as possible. The unstability produces noisy dc signal.

Another source of noise, is the production of unpure FM spectrum. Due to this,

there is an unbalance in the sideband of the FM spectrum which prevents the beat

frequency from vanishing exactly. This residual signal can be detected by the photodiode

and introduces non-zero offset. This can be minimized, by carefully aligning

the polarization of the input probe beam into the EOM and also by the pump-probe

beam allignment. We have found that the optical alignment makes a lot of difference

in bringing the error signal offset to zero. The bandwidth of the current feedback

is 100 kHz and is limited by the DFB laser current driver bandwith (Thorlabs LDC

202). The lasers are locked to the respective spectral lines by modulating the injection

current to the lasers by giving feedback to the modulation input of the current driver

with a bandwidth of 250 kHz. Stabilizing the lasers with the help of temperature

controllers cannot be used, as the temperature controllers cannot stabilize the DFB

laser wavelength better then 30 MHz. As is mentioned before, the feedback circuit

consists of two outputs: the monitor output and the current feedback output. The

current-feedback consists of two paths. One is the high frequency cut-off path, with

cut-off frequency 100 kHz and the other is a 10 Hz cut-off path. If feedback is provided

only through 100 kHz loop, then the laser is locked but it drifts away with time. So to

arrest this slow drift, an integrator type feedback with integration speed of 10 Hz is

added in parallel with the fast response path. The laser can now be stabilized as long

as there is no external interference. The details of the feedback circuit is shown in

Appendix C. The wavemeter and the OSA has been used to monitor simultaneously

the locked wavelength and the mode conditions. The cooling DFB laser is locked

to the 6 2 S 1/2 F=4 to the last cross over transition between the hyperfine structure

levels 6 2 P 3/2 F’=4 & F’=5. The locked signal is shown in Fig. 2.11 along with the

SAS signal for comparison. Figure 2.12(a) shows the comparision of the unlocked

free running laser with the locked signal. Calibration of the locked signal with error

signal as reference has been carried out and a standard deviation (SD) of the laser

frequency variation has been plotted as shown in Fig. 2.12(b). The resulting cooling

laser stability is around 1.75 MHz, less than the natural linewidth of 5.2 MHz of Cs


2.2. The Magneto-Optical Trap (MOT) System 45

atoms, and is enough to cool down the atoms in the MOT.

Similarly, the repump laser is locked to the 6 2 S 1/2 F = 3 to the first cross over

transition between the hyperfine structure levels 6 2 P 3/2 F’=2 & F’=3 of the Cs D 2

transition. For both the cooling and repump lasers, the locking schemes are same with

the difference, only in the components. For repump laser the EOM producing the

optical frequency modulation (FM), is a commercial resonant type phase modulator

with modulation frequency, 10 MHz. Figure 2.13(a) shows a typical SAS signal (black

curve) and the corresponding error signal (gray curve) used for laser locking. The

locking transition is also shown in the figure. Figure 2.13(b) shows the long term

stability of the locked laser and shows the repump laser linewidth estimated using

the SD method for laser frequency variations. The resulting repump laser linewidth

is around 2 MHz.

2.2.4 Optical Setup and Magnetic-Field System for the MOT

Figure 2.14(a) shows the optical setup for the MOT cooling and repump beams. The

frequency of the locked cooling laser is upshifted by 113 MHz using an acoustooptic

modulator (AOM)(Crystal Technology, 3110-120). The cooling beam is detuned by

12 MHz from the transition 6S 1/2 F =4→ 6P 3/2 F ′ = 5. We use a home-built driver

for the cooling AOM. It consists of an oscillator (DST Technology, PCL 130F, 1-130

MHz), which generates a square wave at 113 MHz. The higher harmonics present

in the square wave is filtered out by a low pass filter (Minicircuits, BLP150, DC-

140 MHz, 60 dB supression). The signal is then fed to a high speed RF switch

(Minicircuits, ZASWA-2-50-DR). The RF switch has an integrated TTL driver and

is controlled by an external TTL signal which is the gating signal for the AOM. The

output of the RF switch is amplified by a 1 W amplifier (Minicircuits, ZHL-1-2 W,

34 dB gain) and is then fed to the AOM crystal. To tune the RF power to the AOM,

a variable attenuator (DST, 1-10 dB in 1 dB steps) has been used between the switch

and the amplifier. We achieved high-speed switching and good isolation with this

driver. Similarly, the frequency of the locked repump laser is upshifted by 75.6 MHz

using another AOM (Isomet, 1205C) to be resonant with 6S 1/2 F =3→ 6P 3/2 F ′ =3


Chapter 2. Experimental Techniques 46

(a)

Voltage [V]

0.10

0.08

0.00

-0.10

SAS signal

Error signal

F = 3 -> CO [ F ' = 2, 3 ]

-0.20

-0.02 -0.01 0.00 0.01

Time (s)

Frequency (MHz)

1.0

0.6

0.2

-0.2

-0.6

-1.0

-1.4

-1.8

(b)

Long term stability

-2.2

0 1 2 3 4 5 6 7 8 9

3

Time (s) X 10

No. of Occurances

300

250

200

150

100

50

(c)

FWHM = 2 MHz

0

-2 -1 0 1 2 3 4

Frequency (MHz)

Figure 2.13: (a) The error signal (lower grey curve) of the repump DFB laser observed

at the monitor ouput of the repump locking circuit. For comparison the corresponding

SAS signal is also shown (upper black curve) in the plot. The cross-over transition to

which the repump laser is locked is also shown. (b) Long term stability measurement

of the repump laser: The error signal is observed under locked condition. The laser

is placed at the cross-over resoannce. A labview analog-digital converter card has

been used to measure and record the error signal for this long duration. (c) The laser

linewidth estimation using standard deviation method. The linewidth of the repump

laser is around 2 MHz.


2.2. The Magneto-Optical Trap (MOT) System 47

(a)

To MOT

L

f = 30 cm

Pin hole

400 µm

M

L

f = 5 cm

L

M

M

PBS λ/2

25 cm

M

M

L

f = 30 cm

AOM

+75.6 MHz

AOM

+113 MHz

L λ/2 PBS

f = 25 cm

For locking

L

f = 30 cm

PBS

For locking

λ/2

λ/2

DFB

Repump

Isolator

M

Isolator

DFB

Cooling

M

(b)

CCD 1

(c)

M 5

M 2

λ/4

Current

MOT

CCD 2

M 4

M 3

λ/4

Current

B-field

Coils

λ/4

M 6

M 1

λ/4

Cooling +

Repump Beam

Figure 2.14: (a) Arrangement of the optics for MOT cooling and repump laser, M -

Mirror, L -Lens, PBS -Polarization beam splitter, AOM -Acoustooptic modulator (b)

Optical setup for the MOT system, M-Mirror, B-field - Magnetic field coils, CCD-

CCD camera,(c) A typical CCD view of the MOT fluorescence, taken with CCD 2.


Chapter 2. Experimental Techniques 48

transition. For the repump beam AOM, we use a commercial fixed frequency (75.6

MHz) driver from Isomet.

The upshifted cooling and repump beams are then combined in a polarization

beam splitter (PBS) as shown in Fig. 2.14(a). The combined beam is then expanded

by six times using two lenses of focal length 5 cm and 30 cm respectively. A pinhole

of size 400 µm, placed at the focus of the lens system, acts as a spatial filter for the

combined beam. Figure 2.14(b) shows the MOT optics and the magnetic field (Bfield)

coil arrangements. We use one pass beam configuration for MOT. The expanded

beam goes through three-perpendicular axes and is then reflected back. The windows

of the vacuum chamber are designed with good antireflection coatings to minimize the

imbalance of power in the counter propagating beams. The magnetic field (B-field)

coils used for the MOT are in anti-Helmholtz configuration and produces a B-field

gradient of 10 Guass/cm. In addition to the anti-Helmholtz coils, we use two pairs

of Helmholtz coils in the other two orthogonal axes for fine tuning the MOT position

with respect to the nanofiber. Also, due to the geometry of the chamber and the

nanofiber position, the number of turns and current flowing through each of the anti-

Helmholtz coils are unequal to make the MOT position overlap with the nanofiber in

the vertical direction. A resistively heated alkali metal dispenser source (Saes Getters)

is used to generate cesium atoms for the MOT. The dispenser source is controlled by a

DC current and the generation rate of Cs atoms is highly reproducible as reported in

Ref. [84]. A CCD view of the MOT is shown in Fig. 2.14(c). The overall dimension

of the cloud is around 1 mm. We use two CCD cameras to observe the MOT in

both vertical (CCD 1) and the horizontal direction (CCD 2). The initial alignment

and optimization is done by looking at the CCD-view only. The MOT characteristics

like density and temperature are measured using probe absorption method discussed

in the later sections. The fine tuning of intensity and detuning of the cooling laser

is done based on this measurements. Figure 2.15 shows the schematic diagram and

photograph of the MOT-setup.


2.2. The Magneto-Optical Trap (MOT) System 49

(a)

NF OUTPUT

PORT

Cs Dispenser

Electrical Feedthrough

NF INPUT

PORT

MOT laser beams

Ion pump

Turbo Pump and

Rotary Pump

Nanofiber with MOT-Cs Atoms

(b)

CCD1

CCD2

NF OUTPUT

PORT

B-FIELD

UPPER COILS

WATER

COOLING

VACUUM

CHAMBER

STAINLESS

STEEL TUBE

TEFLON

TUBE

NF INPUT

PORT

FIBER

MOT BEAMS

Figure 2.15: (a) Schematic diagram of the MOT set-up (Top-view). (b) The photograph

of the MOT optical setup. The nanofiber input/output port along with the

teflon tube is shown. The upper B-field coils and the water cooling system can also

been seen. The MOT beam propagation is shown by red arrows. CCD 1 and CCD 2

camera used for aligning the MOT with nanofiber are also shown.


Chapter 2. Experimental Techniques 50

2.3 Optical Nanofiber with MOT Cold Atoms

After realizing nanofiber and MOT, we need to install the nanofiber in the MOTvacuum-chamber.

Figure 2.16 shows the steps for installing nanofiber in the vacuum

chamber. The nanofiber prepared is first fixed on a non-magnetic stainless-steel

holder. Figure 2.16(a) shows the holder with two elevated stages, on top of which the

quartz plates are fixed. The holder is designed in such a way so as not to obstruct

the MOT beams when installed inside the vacuum chamber and also to position the

nanofiber close to the MOT position. The both-ends of the nanofiber are fixed on the

two quartz plates by melting low-temperature glass-preforms (DieMat) using a CO 2

laser (Universal Laser Systems, 15 W). The quartz plates are used because of the

high-sticking probability of glass-preforms. The nanofiber is fixed on to the quartz

plates as shown in Fig. 2.16(b). The holder is connected to one of the flange of the

vacuum chamber as shown in Fig. 2.16(c). The flange is then brought from the clean

booth to the vacuum chamber. During the transfer, the nanofiber is protected from

the surrounding dust with the help of an acryl-cover, to prevent any further loss in

transmission of nanofiber. In the meantime, the vacuum-chamber is leaked with very

clean dust-free Argon-gas to avoid any incoming dust into the chamber. Also care

should be taken that the Ar-gas flux is not too big, to break the nanofiber. The

flange carrying the nanofiber holder is slowly brought towards the vacuum chamber

window and the other end of the fiber is pulled through the opposite flange. The

dust protection cover is removed just before entering the nanofiber in the vacuum

chamber and flange is then bolted to the chamber. The orientation of the nanofiber

is horizontal, in the present experiments. After installation, the stainless steel ports

connected to the fiber holder flange are sealed by low-temperature glass-preforms as

shown in Fig. 2.16(d). A teflon tube is used at the output of the ports to provide

additional support to the fiber particularly at the ends of the stainless steel tube. The

Ar-gas flow is stopped and the chamber is evacuated slowly to avoid any sudden flux

of air that may affect the fiber conditions. After reaching the required vacuum, the

Cs-atom dispenser is also baked gradually to avoid any contaminant deposition on the


2.4. The Excitation Laser Systems and Their Frequency Stabilization 51

fiber. After installation the transmission of the fiber is around 80-85 %. After proper

vacuum conditions are reached, the MOT is prepared and is made to overlap with

the nanofiber using the MOT anti-Helmholtz coils as well as the two additional pair

of Helmholtz coils. Two CCD cameras are used in orthogonal directions to observe

the MOT. A typical CCD view of the MOT overlapped with the nanofiber is shown

in Fig. 2.16(e). The experiments are then carried out.

2.4 The Excitation Laser Systems and Their Frequency

Stabilization

For precision spectroscopy like measurements of excitation and emission spectrum,

we need accurate and stable excitation lasers. We use external-cavity laser diodes

(ECLD) for our excitation lasers. The ECLD system consists of an additional external

cavity along with the internal cavity formed by the end-faces of the semiconductor

material and is basically a Fabry-Perot resonator. The emitting wavelength

of the ECDL is determined by the interplay of the semiconductor gain profile, internal

cavity-modes and external cavity-modes. If the gain profile of the laser is very

broad like in the case of laser diodes, several modes might experience similar gain

and multi-mode emission occurs. Introducing a frequency selective element into the

cavity will give different weight to adjacent internal cavity-modes and there will be

usually one mode, which is the most favored. A grating is the most common frequency

discriminator and it forms an external cavity with the diode. The grating feedbacks

the first-order diffracted light into the diode and couples out the zeroth-order light.

The selected wavelength λ = 2d sin α is determined by the line spacing d of the

grating and the incident angle α, equal to the angle of the first-order diffraction. A

high-feedback of the grating provides more frequency stability, but lowers the output

power. A good compromise is to have a diffraction efficiency of 15 to 20 %. This

configuration with the first order of a grating directly fed back into the laser is called

Littrow configuration. Also another configuration quite often used is Littman-Metcalf


Chapter 2. Experimental Techniques 52

(a)

(b)

Quartz

Holder

Fixing

Screws

Nanofiber

(c)

Vacuum

Flange

(d)

Satinless

Steel Tube

Holder fixing

point

Teflon Tube

Glass Preform MOT+Nanofiber

(e)

Figure 2.16: Nanofiber installation into the vacuum chamber. (a) The nanofiber

stainless steel holding structure. The quartz glass plates on which the nanofiber is

fixed can be seen. (b) The nanofiber is prepared and is fixed on to the quartz plates

of the holder using glass preforms. (c) The vacuum chamber flange to which the

holder is fixed. The nanofiber is then installed inside the chamber. (d) The sealing

of the stainless-steel tube with glass-preforms. The Teflon-tube is finally inserted to

support the optical fiber. (e) The CCD-view of the nanofiber overlapped with the

MOT-atomic-cloud.


2.4. The Excitation Laser Systems and Their Frequency Stabilization 53

type configuration. This type of configuration uses the same principle as Littrow type

but an additional end mirror rotation helps in realizing large range mode-hop-free operation.

The extended cavity offers the possibility of accurate frequency control by

adjusting the cavity length with a piezo-electric crystal (PZT) with frequencies up to

a few kHz. Faster frequency changes can be done by modulating the laser current.

We use two ECLD’s for our excitation laser system. One is a home-built ECLD

system in Littrow configuration (EL1) and the other is a commercial ECLD system

(NewFocus, Vortex 6000) in Littman-Metcalf configuration (EL2).

The EL1 system is locked to the Cs-atomic line using SAS technique and EL2

system is phase-locked to the EL1 laser. Thus EL1 acts as the master laser and EL2

as slave. The Cs D 2 optical transitions to which they are locked are shown in Fig.

2.17(a). Also shown are the upshifting of the laser frequencies using AOM’s. The

optical layout and the locking setup of EL1 is shown in Fig. 2.17(b). The home

built EL1 consists of a diode chip (Eagleyard) and the collimation optics (Thorlabs)

and is mounted on a customized home made base structure designed to include the

external cavity and the water-cooling based heat sink. For the external cavity and its

tuning, we use gold coated diffraction grating (Optometrics) and piezo-electric crystal

(PZT, NEC-Tokin) respectively. We get around 40 mW power which is enough for the

present experiments. The laser is quite stable and is easily tunable. The temperature

tuning of the base setup by a Peltier element allows for large and crude tuning but

has a very slow response. For smaller range tuning, within several GHz and better

response time, we tune the external grating using PZT. For faster response and more

fine-tuning, we employ laser current modulation through current driver. The current

tuning is done after locking the laser with PZT feedback, as current also determines

the power. The PZT and current modulation bandwidth is around 1 kHz and 250

kHz respectively. The current feedback is limited by the bandwidth of the current

driver (Thorlabs LDC 200). The feedback circuit, as discussed before, consists of

low-pass filters. Figure 2.18 shows the SAS signal and the locking performance. The

laser stabilty is within 1 MHz and can be maintained for several hours. In the next

paragraph, we discuss locking of EL2 to EL1 using the phase-locking technique.


Chapter 2. Experimental Techniques 54

(a)

+80 MHz

'

F =5

251 MHz

201 MHz

151 MHz

Excitation 1

Transition

9.2 GHz

+75.6 MHz

Excitation 2

Transition

F=4

'

F =4

'

F =3

'

F =2

F=3

6 P3/2

6 S1/2

(b)

For Excitation

AOM

+80 MHz

GP

M

PBS

PBS λ/2

For Phase Locking

Isolator

AMP

Excitation

Laser 2

For Excitation

L

25 cm

For Feedback

PD

Probe

L

10 cm

Cs Cell

AOM

+75.6 MHz

Pump

L

25 cm

M

EOM

L

15 cm

GP

FM

PBS

λ/2

M

M

λ/2

PBS

PBS

M

λ/2

Isolator

Febry-Perot

Etalon

Excitation

Laser 1

AMP

M

Figure 2.17: (a) The schematic diagram of the optical transitions to which the reference

and the excitation lasers are locked. Also shown are the upshifting of frequencies

by the AOM’s. (b) The optical layout of the excitation lasers. Also shown is the SAS

setup used for locking the excitation laser, EL1.


2.4. The Excitation Laser Systems and Their Frequency Stabilization 55

(a)

(b)

Figure 2.18: (a) The SAS signal of the excitation laser EL1. (b) The error signal under

locked condition is shown both for PZT feedback as well as PZT+current feedback.

PZT

Driver

Feedback

Circuit

LD

Driver

Direct Feedback to LD Chip

Buffer

Phase

Comparator ~ 575

MHz

Prescaler 2

4

~ 2.3 GHz

Prescaler 1

4

Buffer

9.2 GHz

DC

Block Detector

G.L.P

P.B.S

λ/2

Slave

Laser

Local

Oscillator

Spectrum Analyzer

Master

Laser

Figure 2.19: Schematic diagram of the phase-locking setup of the excitation laser EL2

with respect to EL1, at 9.2 GHz.


Chapter 2. Experimental Techniques 56

0

-20

Span = 10 MHz

RBW = 3 kHz

CF = 9.2 GHz

0

-20

Span = 1 MHz

RBW = 300 Hz

CF = 9.2 GHz

Power (dBm)

-40

-60

Power (dBm)

-40

-60

-80

-80

Power (dBm)

0

-20

-40

-60

-5 -4 -3 -2 -1 0 1 2 3 4 5

Frequency (MHz)

Span = 100 kHz

RBW = 100 Hz

CF = 9.2 GHz

Power (dBm)

-10

-30

-50

-400 -200 0 200 400

Frequency (KHz)

Span = 1 kHz

RBW = 10 Hz

CF = 9.2 GHz

3-dB Bandwidth < 10Hz

-80

-70

-100

-50 -40 -30 -20 -10 0 10 20 30 40 50

Frequency (KHz)

-90

-400 -200 0 200 400

Frequency (Hz)

Figure 2.20: The phase-locked beat-signal between excitation lasers, EL1 and EL2,

shown at four different frequency spans of the spectrum analyzer.


2.4. The Excitation Laser Systems and Their Frequency Stabilization 57

The EL2 is phase locked to the EL1 master laser [85, 86, 87, 88]. For phase locking

we use the beat-frequency (at frequency 9.2 GHz) between the master and the

slave laser and compare it with a stable local-oscillator signal using a digital phase

comparator. The phase-locking scheme involves scaling down of the beat-frequency

by 16 times using a prescaler, and then compare the down converted frequency with

a stable 575 MHz oscillator. The prescaling ratio should not be too large because

the strength of the error signal reduces with increase in the prescaling ratio. Figure

2.19 shows the schematic diagram of the phase locking setup. The beat signal between

the master and the slave laser is detected using a high-speed PIN photodiode

(Hamamatsu, G9287-14). The detector has a fiber coupler input and consists of an

integrated preamplifier. To remove any unwanted dc signal, a DC block has been used

after the detector. The DC block output is fed to the input of the prescaler block.

The prescaling of the beat frequency is carried out in two steps. The beat frequency

is first scaled down by a factor of 4 by prescaler 1. One of the output of the prescaler

1 goes to a spectrum analyzer (Advantest) for monitoring the beat signal and the

other output goes to the next prescaler. The prescaler 2 scales down the frequency

by another 4 times and the beat frequency now becomes 575 MHz. The 575 MHz

signal is compared with a local oscillator signal of 575 MHz (Agilent Technology)

using a digital phase comparator (DST Technology). The comparator then gives an

error signal proportional to the phase and frequency difference between the two input

signals. The error signal is then integrated in different time scales and then fed back

to the slave laser (EL 2) using three different feedback channels. These three channels

are the PZT feedback (bandwidth ∼1 kHz), the feedback through current driver

(NewFocus Vortex 6000 driver, bandwidth ∼1 MHz) and the feedback directly to the

laser diode (LD) chip itself (∼100 MHz). The bandwidth of PZT feedback is limited

by the respone time of the grating structure with which the PZT is attached. The

response time of the LD driver feedback is limited by the LD driver itself. So the wide

bandwidth direct feedback to the LD chip is very crucial for a stable phase locking.

The beat signal is recorded using the spectrum analyzer and Fig. 2.20 shows the beat

signal under phase locked condition, for four different frequency spans. The measured


Chapter 2. Experimental Techniques 58

3 dB bandwidth of the phase locked beat signal is less than 10 Hz and is limited by the

resolution-bandwidth of the spectrum analyzer. The frequency stability of the slave

laser depends on the frequency stability of the master laser and the local oscillator

signal. We have used a common grounding for the detector, the locking circuit, the

prescaler and the phase comparator. Special cables has been used for carrying the RF

signal between different components of the phase locking technique and their length

has been kept small to reduce any loss due to signal attenuation. Also, we have found

that noise from power supplies used for driving different components can also affect

the locking conditions. We use a commercial low-noise power supply (Kenwood), for

this purpose. The phase-locking technique is quite robust and we can easily tune the

laser frequency just by tuning the local-oscillator frequency.

For the present experiments, to manipulate the surface of the nanofiber, we use

a free-running UV laser (Nichia laser) at a wavelength of 407 nm. It is mounted on

a commercial module (Data Systems, ALTH-103RS) with an integrated temperature

controller and is driven by a LD and temperature controller system (Data Systems,

ALP-7033CA). The maximum available power is 20 mW and is sufficient for the

present experiments. The beam diameter of the UV laser used for the experiments

is around 2 mm and is enough to cover the MOT atom cloud overlapped with the

nanofiber.

2.5 The Detector, Timing and Photon-Correlator

Systems

In most of the present experiments, the MOT beams are switched on and off periodically

and the cold atoms around the nanofiber are excited by switching on the

excitation beam, which is irradiated perpendicularly to the nanofiber. The laser

beams are switched on and off using AOMs. The fluorescence photons from the

Cs-atoms coupled to the guided-modes of the nanofiber are detected at the ends of

the optical fiber using single photon counting modules (SPCMs). The output of the


2.5. The Detector, Timing and Photon-Correlator Systems 59

SPCM is a digital pulse and is counted by a photon counting board. Both the SPCM

and the counting board are operated in gate mode and photon counts are recorded

in a personal computer (PC). All the timing sequence for AOMs, SPCMs, and the

counting-board are generated using a timing-circuit. The details of the SPCMs, the

counting-board and the timing-sequence generator are discussed in the next section.

Avalanche Photo-Diodes, Counting Board and Timing Signals for the Experiments

We use silicon avalanche photodiode (APD) based detector for our fluorescence measurements.

As the number of atoms emitting fluorescence in the guided-modes of the

nanofiber is very small in number, the fluorescence power expected at the ends of the

optical fiber is in the femtowatt (fW) range. So a high-sensitive detector is needed

for this purpose. APDs are very suitable for the case of low-power light detection

and can operate in single-photon-counting-mode with the help of an active quenching

circuit. We use a commercial APD module (PerkinElmer, SPCM-AQR-FC) with an

integrated thermoelectric cooler and temperature controller. The SPCM has a fiber

FC input which makes it convenient to directly connect the commercial single-mode

fiber with FC connector which is spliced to the nanofiber. The SPCM gives a 35 ns

pulse for each detected photon and has a dead-time of 50 ns. The quantum efficiency

of detection is 45 % at our fluorescence wavelength of 852 nm. It has a saturation

count of around 15 million counts per second (Mc/s). A gating function is provided

in each module which is useful for the present experiments when we expect photon

during a particular time window.

The output of the SPCM is counted using a photon counting-board (Hamamatsu,

M8784). The counting-board is a standard PCI board and is installed in a PC. The

counting board operates in gate-mode and is controlled by a LabView based software

program installed on the PC. The photon counts are recorded on the PC.

All the timing sequence for the AOMs, SPCMs, and counting board are generated

using a timing-circuit. Figure 2.21(a) shows the schematic diagram of the timingcircuit.

The timing-circuit mainly consists of mono-stable multi-vibrators triggered


Chapter 2. Experimental Techniques 60

by a digital pulse generator (Stanford Research, DG 535). The Start/Stop signals

for a measurement run is given by the counting board, which triggers the DG535

through the timing-circuit. The DG535 then gives the trigger signals for start and

stop of each gate and also a retrigger signal to repeat the cycle. The outputs of

the multivibrator circuit provide the gate signals with appropriate delays for all the

AOMs and the counting-board. The gating signal for SPCM is generated by the

DG535 generator via a MOSFET-circuit to pull-up the gate voltage levels. There is

a limitation to the minimum gate pulse-width which can be generated by the timingcircuit.

So for experiments requiring faster switching times, we use a commercial

digital and analog signal generator (National Instruments) shown in Fig. 2.21(b). It

consists of two PCI based cards and is installed on a PC (PC2). One for digital pulse

generation (PCI6542) and another for analog signal generation (PCI 6733). The

initial triggering is from the counting board and is same as that for multivibrator

based timing circuit. The PCI 6542 card is controlled by a software, Signal express

and PCI 6733 is controlled by a LabView program with digital-retrigger option. The

PCI 6542 after receiving the first trigger pulse from the counting board generates

the gate pulses for the AOMs, SPCMs, counting board and the trigger signal for

PCI 6733. The PCI 6733 can generate any type of arbitrary waveform shape and is

retriggerable to keep it in sync with the PCI 6542.

Time-Correlated Single Photon-Counting Systems

The temporal information of photons coming from atoms via laser induced fluorescence

is a very powerful technique in spectroscopic studies. The histogram of the

arrival times of photons with respect to the arrival time of the first photon, known

as two time photon correlation or coinicidence measurement, reveals information like

number of atoms, life-time of the atoms, atom dynamics in different types of potentials

etc.. In addition to it the coincidence measurement gives information about the fundamental

first- and second-order correlation functions. For the present experiments

we have carried out coincidence measurements to determine the number of atoms, to

find the life-time of the atoms in the observation region around the nanofiber, and


2.5. The Detector, Timing and Photon-Correlator Systems 61

(a)

LABVIEW

CONTROL

PERSONAL COMPUTER

COUNTING BOARD

SPCM OUTPUT

OVERALL START/STOP

TRIGGER

COUNTING

BOARD GATE

TRIGGER

DG535 DIGITAL PULSE/DELAY

GENERATOR

GATE START

GATE STOP

SPCM GATE

RE-TRIGGER

MOSFET

MULTIVIBRATOR CIRCUIT

GATE PULSE

SPCM’S

MOT AOM

DRIVERS

TRAPPING LASER

AOM DRIVERS

EXCITATION LASER

AOM DRIVER

EXPERIMENT MODULES

(b)

PERSONAL COMPUTER 1

LABVIEW

CONTROL

COUNTING BOARD

Gate Pulse

1st Trigger

PERSONAL COMPUTER 2

DAQ DIGITAL WAVEFORM GENERATOR

PCI 6542

64 MBit/ch., 100 MHz

CONNECTION CABLE

DIGITAL WAVEFORM

EDITOR

SIGNAL EXPRESS

ANALOG WAVEFORM

CONTROL

Trigger

DAQ ANALOG O/P DEVICE

PCI 6733

CONNECTION

CABLE

CONNECTOR BLOCK

SMB 2163

CONNECTOR BLOCK

BNC 2110

Gate Pulses

VOLTAGE RAMP GENERATOR

AOM FREQUENCY SHIFTER

MOT AOM

DRIVERS

SPCM’S

TRAPPING LASER

AOM DRIVERS

EXCITATION LASER

AOM DRIVER

EXPERIMENT MODULES

Figure 2.21: Schematic diagram of the timing circuit for generating timing signals

for the experiments. (a) Using multivibrators. (b) Using the NI digital and analog

signal generators.


Chapter 2. Experimental Techniques 62

to derive the information of LIF emission spectrum by combining the coincidence

measurements with optical heterodyne technique. The combined optical heterodyne

technique with photon correlation spectroscopy is discussed in details in Chapter 3.

We use a commercial time-correlated single photon counting system (PicoQuant,

TCSPC-TimeHarp 200) for measuring the photon coincidences. It is a PCI-Board

based system and is installed on a PC. It has 2 channels of input and it records the

photon arrival times in both the channels and gives directly the photon coincidences.

It works in two primary modes. One is oscilloscope-mode and another is integrationmode

(to integrate the data for better signal-to-noise ratio). A customized LabView

software has been used to read the data recorded in the integration-mode. The time

resolution of measurement is 31 ps. It operates in single start/stop mode that is after

recording the first photon in one channel it waits for the arrival of next photon in the

second channel and during this time it ignores any photon that arrives in the first

channel. For low photon count rates, the single start/stop mode works well but with

increase in the photon counts there is a systematic pile-up error in the recorded data

[89]. To remove this type of error, the solution is to record all the photons which

arrive at both the channels. For this purpose we use another type of TCSPC system

(PicoQuant, TCSPC-PicoHarp 300) which records all the photon arrival times. It can

also operate in integration mode. The time resolution for each channel used for the

present experiments is 4 ps. A program written in C is used to read the recorded data

and to derive the photon coincidences. The duration for which PicoHarp can record

the photon arrival times depend on the memory of the PC itself. Hence, coincidence

measurements for long delay-time is possible.

2.6 Density and Temperature of MOT-atoms

Before starting the atomic fluorescence measurements we need to characterize the

MOT by measuring the density and temperature of the MOT-atoms. We use probe

absorption technique for this measurements [90, 91, 92]. The experimental scheme is

as follows. We use EL2 as the probe beam which is focused on to the MOT-atomic


2.6. Density and Temperature of MOT-atoms 63

Figure 2.22: Density measurements of MOT-atoms. The figure shows the probe

absorption signal. The black-curve shows the probe transmission at different time

instants. The red-curve denotes the background light-level in the absence of the

probe.

cloud using a lens of focal length 450 mm and the probe beam diameter at the position

of the MOT is around 200 µm. The intensity of the probe beam at the focus is around

0.075 mW/cm 2 , much less than the saturation intensity of Cs atom and has negligible

mechanical pushing-effect on the atom. After passing through the MOT-cloud the

probe beam is again focused on to a detector (NewFocus, Model 2001), using a lens

of focal length 50 mm. In order to avoid saturation of the MOT-atoms due to strong

MOT trap beams, the MOT beams are switched-off for 10 ms periodically at an

interval of 800 ms. The probe beam is kept always on for this measurements and

the absorption signal is recorded using an oscilloscope. A typical absorption signal is

shown in Fig. 2.22. During the on time for MOT beams, the probe absorption is very

small due to saturation. At the starting of the dark period (MOT beams are off) the

probe absorption is maximum, and gradually with the expansion of the MOT cloud

the absorption decreases and at the end of the dark period the probe absorption is

minimum. The density of the cloud can be derived from the strength of the absorption

signal. From the relation, I = I o exp(− √ πσnr o ) where I o is the incident intensity, I is


Chapter 2. Experimental Techniques 64

the transmitted intensity, σ = 3λ2 =3.63 × 2π

10−9 cm 2 is the absorption cross section,

r o is the 1/e-radius of MOT, the number density n of MOT-atoms can be derived. For

temperature estimation, the probe is placed either above or below the MOT-cloud.

As a result, the absorption signal-peak is delayed depending on the arrival time of

the atoms to the probe beam. From the knowledge of the separation of the probe

beam from the atom-cloud, we can estimate the peak-velocity distribution of the

cloud and hence the temperature of the MOT-cloud. The density and temperature

depends on the MOT cooling beam detuning from the atomic transition, the MOT

beam intensities, and the dispenser current. For the present experiments, we use a

cooling beam detuning of 12 MHz and a typical dispenser current of 5.2 A. At this

condition, the MOT-atom density is around 10 10 atoms/cm 3 and the temperature of

the cloud is around 100 µK.


chapter 3

FLUORESCENCE SPECTRUM OF STRONGLY DRIVEN

ATOMS

3.1 Introduction

As discussed in Chapter 1, resonance fluorescence of atoms consists of two main contributions,

the elastic scattering and the inelastic scattering components. The elastic

contribution comes from the well-known Rayleigh scattering and the inelastic component

consists of fluorescence scattering. If the driving field is weak, the elastic

scattering part dominates and if the driving field is strong, the inelastic part dominates.

To investigate the atomic fluorescence we perform laser-induced fluorescence

(LIF) spectroscopy [1, 2, 4]. In the present work, we investigate the fluorescence

scattering for the case when the excitation intensity is high and therefore the atoms

are strongly driven. The LIF spectroscopy is categorized into two methods. One is

the excitation spectroscopy and the other is emission spectroscopy.

Regarding the measurement method of emission spectrum, two very high resolution

methods are well known. One is the optical heterodyne (OHD) spectroscopy, and

66


3.1. Introduction 67

the other is photon correlation (PCR) spectroscopy. The essence of the OHD spectroscopy

is to measure the beat signals between a coherent local-oscillator light and

the fluorescence light which is emitted into the same single spatial-mode as that of the

local oscillator. On the other hand, the PCR-spectroscopy is based on photon correlation

measurements with the Hanbury Brown-Twiss (HBT) setup. For single-mode

observations, the intensity correlations can be expressed by the first-order correlation

function in the many-emitter limit. Hence, one can obtain the emission spectrum

through the PCR measurements by Fourier-transforming the obtained first-order correlation

functions [2, 1]. Both the OHD and PCR methods readily realize very high

spectral resolution, higher than the natural linewidth. The OHD method has been

used for the fluorescence spectrum measurement of many-atom [22, 23] and single-ion

systems [93, 94]. However, none of the above methods have been applied to measure

the fluorescence spectrum of few atoms, which is distributed in a wide frequency range

wider than the natural linewidth of atoms. This is due to the fact that these methods

require single-spatial-mode observations, which demands many atoms to have a

measurable fluorescence photon number. Moreover the PCR method is valid only

for multi-emitter system. Recently, Hong etal. have proposed to combine both the

OHD and PCR methods to realize high resolution and high sensitivity. Using such

a combined method they have demonstrated the measurement of the spectrum of an

extremely weak coherent light [95]. If such a combined method can be extended to

measure fluorescence spectrum of a small number of atoms, it would be very beneficial

to laser spectroscopy. However, it still requires efficient single-mode collection

of few-atom emission. So, we have combined the nanofiber method of single-mode

fluorescence detection with the OHD technique and PCR spectroscopy for the emission

spectrum measurements. The emission spectrum has been investigated for both

on-resonant and off-resonant excitations.

As mentioned in Sec. 1.4, atoms emitting fluorescence in the guided-modes lie

very close to the nanofiber surface, closer than the emission wavelength λ, and are

subjected to atom-surface interactions. The atom-surface interactions can be modified

by irradiating the MOT-atoms overlapped with the nanofiber, with an UV laser


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 68

[42]. The UV laser irradiation keep the atoms from falling into the surface potential

and the near-surface atoms behave almost like free-atoms around the nanofiber.

The lineshape of the excitation spectrum, measured under this condition, shows a

Lorentzian behavior with a very small tail in the red detuned side (red-tail). The

small red-tail has been attributed to the photoassociation (PA) process for atoms

making transition from free-ground states to the bound excited states. We will discuss

in details the PA process and the effect of UV laser irradiation in Chap. 4. In

this chapter, as a first step towards the demonstration of fluorescence emission spectrum

measurements using nanofiber, we carry out the LIF measurements under this

free-atom conditions [42]. The emission spectrum should give us information about

the behavior of such near surface atoms and can confirm whether the atoms behave

like a free-space atoms by comparing the observed spectrum with the known freespace

atom spectrum. In the next section we discuss first the excitation spectrum

measurements. Next, we estimate the number of atoms around the nanofiber, which

emits fluorescence in the guided-modes of the nanofiber by measuring the correlations

between the photons emitted into opposite directions of the nanofiber [44]. We then

discuss the measurements of fluorescence emission spectra of atoms.

3.2 LIF Excitation Spectrum Measurements : Experimental

Procedures and Results

We discuss in this section the excitation spectrum measurements, under the condition

when the near surface atoms behave like a free-space atoms. As mentioned earlier,

the free-atom condition has been maintained during the measurements by the use of

an external UV laser (407 nm) [42]. The UV laser intensity of 40 mW/cm 2 is used to

irradiate the MOT-atoms overlapped with the nanofiber, during the measurements.

Figure 3.1(a) shows the schematic diagram of the experimental setup. As discussed

in Sec. 1.3, the coupling efficiency of fluorescence in the guided-modes for Cs atoms is

maximum when the diameter of the nanofiber is ∼400 nm. In this thesis, we perform


3.2. LIF Excitation Spectrum Measurements : Experimental Procedures and Results 69

(a)

Excitation Laser

Fluorescence

Photons

Nanofiber

Cold Cs atoms in MOT

APD

Photon-

Counting

Board

PC

(b)

Cooling

Laser

OFF

ON

Repump

Laser

200ns

OFF

ON

Excitation

Laser

ON

OFF

Photon

Counting

1.6µs

ON

OFF

10µs

200µs

Figure 3.1: (a) Schematic diagram of the experimental setup for the excitation spectrum

measurements. (b) The timing sequence used for the present experiments. The

signals are generated using the multivibrator based timing circuit, as discussed in

Chapter 2.


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 70

F’ = 5


F = 4

Figure 3.2: Fluorescence excitation spectrum measured (black square dots) through

the nanofiber for the Cs D 2 closed cycle transition 6S 1/2 F =4→ 6P 3/2 F ′ = 5. Detuning

(∆) of the excitation beam is measured with respect to the atomic resonance,

as shown in the inset. The solid gray curve is the Lorentzian fit of the observed data.

The excitation beam intensity is 1 mW/cm 2 . The spectrum has been background

corrected. The arrows show the detuning (a) ∆ = -15 MHz, (b) ∆ = -6 MHz, (c) ∆=

0 MHz, and (d) ∆= +15 MHz, at which the emission spectrum has been measured

as will be discussed in Section 3.5.


3.2. LIF Excitation Spectrum Measurements : Experimental Procedures and Results 71

all the experiments using nanofibers of diameter ∼400 nm. The diameter of the

nanofiber is 400 nm ± 30 nm over the length of about 2 mm. The dispenser current

(I d ) (for generating Cesium atoms for the MOT), used for the present measurements

is 5.2 A and is kept the same for all the fluorescence spectra measurements unless

otherwise specified. The dispenser current of I d =5.2 A has been chosen based on

MOT density measurements as discussed in Sec. 2.6, to have considerable number

of atoms emitting fluorescence in the nanofiber guided-modes. The experiments are

performed by overlapping cold Cs atoms with an optical nanofiber and detecting the

fluorescence photons emitted into the guided-modes of the nanofiber. Figure 3.1(b)

shows the timing sequence used in the present experiments. Experiments are carried

out, by switching off MOT beams for an observation period of 10 µs in every 200

µs and repeating this process for many cycles. For the initial state preparation of

the atoms, the MOT repump beam is switched off 200 ns after the cooling beam,

during each observation period so that any residual atoms in the Cs D 2 F = 3

hyperfine ground state can be pumped to the F = 4 ground state. In the present

experiments, the excitation laser is tuned to F =4↔ F ′ = 5 transition, which is

a closed cycle transition, and the atom behaves as a two-level system. During the

observation period of 10 µs, atoms around the nanofiber are excited by a laser beam

irradiated perpendicular to the nanofiber in the travelling-wave configuration. Such a

timing sequence has been chosen to get the maximum amount of fluorescence during

each cycle of MOT on- and off-period, which depends on the present experimental

conditions like MOT loading time and the decay time. In the present work, the timing

sequence used for all the measurements are identical. The excitation beam, derived

from EL2 laser as discussed in Sec. 2.4, is elliptically focused onto the nanofiber

with a waist size of 1 mm along the fiber axis and 0.5 mm perpendicular to the fiber

axis. The excitation beam is linearly polarized with polarization axis perpendicular

to the fiber axis. The excitation laser frequency is tuned across the Cs D 2 transition

F =4→ F ′ = 5, to measure the excitation spectrum. The atomic fluorescence

coupled in the guided-modes of the nanofiber is detected using an APD. The detected

photon is then counted using a photon counting board (Hamamtsu, M8784) and


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 72

recoreded on a personal computer (PC). Figure 3.2 shows the measured excitation

spectrum (black square dots). We have fitted the observed curve using a Lorentzian

curve (gray solid line). The excitation spectrum does not show a simple Lorentzian

spectrum observed in free space, but shows slightly asymmetric spectral shape shaded

in the red side due to atom-surface van der Waals (vdW) interaction [42]. The small

red-tail has been attributed to photoassociation process due to free-atoms. The full

width half maximum (FWHM) linewidth of the spectrum is 8.7 MHz ± 0.2 MHz,

which is more than the natural linewidth of Cs atom (5.2 MHz).

The increase in the linewidth can be explained by the following mechanisms. Due

to QED-effect there is an increase in the linewidth by about 0.6 MHz [35, 40]. The

effect of the power broadening on the linewidth is around 1.9 MHz. The Doppler

broadening of Cs atoms trapped in a MOT at 100 µK is 117 kHz. In addition to the

above mechanisms, the vdW potential also leads to an increase in the linewidth by

about 1.5 MHz [61]. Including all the above effects, we expect a linewidth of 9.3 MHz

FWHM, which shows reasonable agreement with the observed value.

There can be seen slight asymmetry around, ∆= -10 to -25 MHz. One can see

some modulations on top of the asymmetric part, but these modulations are not

reproducible within the present measurement accuracy. The peak of the spectrum

is shifted by -1.9 MHz. The shift includes a measurement error of 1 MHz, which

is due to the stability of the excitation laser. The fluorescence emission spectra are

measured by setting the excitation beam frequency at four different detunings around

the atomic resonance as marked by (a)-(d) in Fig. 3.2.

The typical photon counting rate at one end of the nanofiber for parameters

shown in Fig. 3.2 is 2.8 × 10 5 counts/s. Following the equation shown in Ref. [40],

n p = nRη fiber Tη D , we estimate the average coupling efficiency of fluorescence into

the nanofiber guided-modes. The parameter n p is the fluorescence photon counts, n

the average atom number, R the atomic scattering rate, η fiber the average coupling

efficiency of fluorescence into nanofiber guided-modes, T is the effective transmission

of the fluorescence photons through the signal fiber-line which includes the nanofiber

transmission and the losses associated with various optics and fiber couplers and η D


3.3. Atom-Number Estimations 73

is the quantum efficiency of the APDs. T and η D are 12% and 45% respectively.

The number of atoms, n ∼ 14 and the atomic scattering rate R is estimated as

1.7 × 10 7 s −1 with a saturation intensity of 2 mW/cm 2 . For the above calculation

we used an effective spontaneous emission rate of 3.6 × 10 7 s −1 which includes the

QED-enhancement factor [35, 40]. Thus we obtain the average coupling efficiency

into one end of the nanofiber guided mode η fiber ∼ 2.3 % . In the next section, we

find out the number of atoms which contributes to the fluorescence into the guided

modes of the nanofiber.

3.3 Atom-Number Estimations

Atoms lying within a distance of wavelength from the nanofiber can only be able

to efficiently channel their fluorescence in the guided-modes of the nanofiber. All

the fluorescence spectra presented in this thesis are measured under the constant

atom-number conditions. This is done by fixing the MOT-preparation parameters.

Assuming an observation volume around the nanofiber and by knowing the density

of MOT-atoms, we can estimate the average atom number which couple their fluorescence

in the guided modes. But, recently a more precise method of estimating the

atom number, based on photon correlation measurements has been proposed by our

group [44, 96]. The key point of the method is to measure the photon (intensity) correlations

for fluorescence emitted into opposite direction of the nanofiber, under the

travelling-wave excitation condition. We consider the case where the atom-position

distribution is random and the atom number has a Poissonian distribution. The

phases of photons emitted by different atoms are random and the total fluorescence

field can be written as the sum of the fields emitted by individual atoms. For simplicity,

we consider a single polarization of the guided field. For the measurement of

correlations between photons coupled into opposite directions of the nanofiber, the

intensity correlation 〈I(t)I(t + τ)〉 is simply governed by the normalized second-order

correlation function g (2) (τ) as following [44, 96],


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 74

(a)

Excitation Laser

Nanofiber

Cold Cs atoms in MOT

MOT

F’ = 5 Cs D 2

line

F = 4

Fluorescence

Photons

APD, D1

APD, D2

FC

Correlator

FC

(b)

(c)

Coincidences / min.

Figure 3.3: (a) Schematic of the experimental setup for measuring photon correlations

coupled into opposite direction of the nanofiber. The excitation laser is resonant with

the Cs D 2 transition F =4→ F ′ = 5 as shown in the inset. MOT: Magneto-Optical

Trap, FC : Fiber Coupler, APD: Avalanche Photo-diode. The correlator used in

the experiments is a commercial time-correlated single photon counting system from

PicoHarp, as discussed in Chapter 2. (b) Measured correlations / minute (gray curve)

between photons emitted into opposite ends of the nanofiber with respect to time

delay, τ. The black curve is the theoretical fit of the correlation signal, as shown in

Eq. 3.1. (c) Plot of the observed correlations (gray curve) for long time delay. The

correlations decay with time. The time period of this decay has been found by fitting

the observations with an exponential decay curve. The decay time is ∼ 2 µs, which

is the dwell time of the atoms around the nanofiber.


3.4. LIF Emission Spectrum Measurements : Experimental Procedures 75

〈I(t)I(t + τ)〉 ∝ng (2) (τ)+n 2 µ 0 (3.1)

where I is the intensity of the fluorescence field emitted by all the atoms combined

and n is the average atom number. 〈...〉 denotes the time average and τ the delay

time. The parameter µ 0 depends on the mode profile function of the guided modes

and its value is determined experimentally as µ 0 = 0.36 [44]. The details of the above

equation are given in appendix A.

The schematic diagram of the experimental setup is given in Fig. 3.3(a). The

excitation beam intensity is 40 mW/cm 2 . The opposite-end correlations are measured

with APDs, D1 and D2. The observed correlations are displayed in Fig. 3.3(b) for

delay time of ±100 ns. We have fitted the observed curve using Eq. 3.1 to obtain

the average atom number n by assuming the theoretical form of g (2) (τ) as given in

Appendix A [2, 43]. The fitting has led to an average atom number of n= 14± 2. In

Fig. 3.3(c), we plot the observed correlations (gray curve) for long time delay. The

correlations decay with time. The decay time is ∼ 2 µs, which is the dwell time of

the atoms around the nanofiber. In the following section we discuss in details the LIF

emission spectrum measurements of this free-atoms.

3.4 LIF Emission Spectrum Measurements : Experimental

Procedures

We first discuss the measurements of the emission spectrum utilizing separately the

optical heterodyne (OHD) technique and photon-correlation (PCR) spectroscopy. We

discuss the limitations of these techniques for the measurement of LIF emission spectra

of around 14 atoms. We then introduce the combined method of OHD and PCR

spectroscopy for the measurement of the emission spectrum. We discuss in details

the theory and experimental procedure of this combined method.


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 76

3.4.1 Optical Heterodyne Technique

OHD technique is a widely used method for detecting very weak-signals and for measurements

requiring high spectral-resolution. A spectral-resolution better than the

natural linewidth of atoms is regularly achieved using OHD compared to techniques

like grating based spectrometer or Fourier-transform infra-red (FTIR) spectrometer.

In this section, we discuss the OHD technique for spectrum measurements of a small

number of atoms.

A single Cs atom driven by a strong resonant laser light emits an average fluorescence

power of ωΓ 0 /2 ≈ 3 pW (in the entire spectrum), where Γ 0 is the natural

linewidth, Γ 0 =2π× 5.2 MHz for cesium atom. Assuming the fluorescence from a

small number of atoms (∼14) is distributed within a spectrum of bandwidth (BW)

5.2 MHz and an overall single mode detection efficiency of our nanofiber system to

be ∼10 −3 , the sensitivity required to detect the atoms is ∼ 0.02 fW/ √ Hz. The overall

detection system includes the quantum efficiency of the detectors, losses due to

nanofiber transmission and the other related optics.

The OHD technique is a basically a photocurrent (analog) measurement based

technique and is often used to detect very low-signal power distributed in a wide

frequency bandwidth [22, 23]. The technique involves mixing of the weak signal to be

meausured with a strong local oscillator (LO) signal usually derived from the same

laser to cancel out noise fluctuations of the laser itself, to get a strong signal at the

beat frequency. The signal information is contained in the beat frequency. The beat

signal power is given by P beat = √ P signal × P LO , where P signal and P LO are the power

of the signal and the LO respectively. So as P LO increases the beat signal power also

increases. But there is a limit on the increase of P LO , as shot noise of LO laser (shot

noise ∝ P LO ) increases with the P LO and it increases the background noise when

detected by a photodiode detector. So experiments are performed in the limit of

the shot noise maintained just greater than the detector noises (Johnson noise, dark

current noise etc.). Also the LO power is limited by the saturation of the detector

itself which is mainly because of the saturation of the low-noise pre-amplifier used in


3.4. LIF Emission Spectrum Measurements : Experimental Procedures 77

the detector.

First to have an estimate of the detection sensitivity, we have tried to measure the

beat signal between two lasers phase locked with each other (∼10 Hz BW). The details

of the experimental setup is given in Appendix B. The beat signal width is limited

by the stabilty of the acousto-optic modulator (AOM) driver which is around 10 kHz.

We use a temperature controlled detector based on APD (Hamamatsu C4777, NEP-

80 fW/ √ Hz, 0.8 µW saturation power, 100 MHz bandwidth), for the beat signal

measurement purposes. The detector output is connected to a spectrum analyzer

(Rohde & Schwarz, FSL-3). The minimum signal level detected using this set up

with signal-to-noise (S/N) ∼ 1 is around 2.5 pW distributed in a frequency range

of 10 kHz. The sensitivity acheived is 100 fW/ √ Hz. It is less than the sensitivity

required for the spectrum measurement of 14 atoms. To improve the signal power

detection we have introduced another phase sensitive dectector (Lock-in Amplifier, NF

Electronics, 5610 B) in the setup. We modulate the AOM with a function generator

and use it as a reference for the lock in amplifier. The modulation frequency of 20 Hz

has been selected because that is the maximum frequency by which the MOT cloud

can be modulated (moving across the nanofiber) without any big difference in atomic

fluorescence signal level. With phase sensitive detection the minimum signal power

that can be detected is around 55 fW distributed in a 10 kHz bandwidth with a S/N of

∼1. The achieved sensitiy is around 0.55 fW/ √ Hz and is still not enough for emission

spectrum measurements. The details of the setup and the results are shown in the

Appendix B. In the next section we discuss the emission spectrum measurements

based on the digital photon-counting based photon correlation spectroscopy.

3.4.2 Photon Correlation Spectroscopy

We briefly describe the theoretical outline of the present few-atom fluorescence spectrum

measurements using nanofiber. The emission spectral density S(ω), can be

directly obtained from the Fourier transform of the first-order correlation function

〈E ⋆ (t)E(t + τ)〉 of the photon field E(t) [1, 2] as,


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 78

S(ω) = √ 1 ∫ ∞

〈E ⋆ (t)E(t + τ)〉e iωτ dτ. (3.2)


−∞

where 〈...〉 denotes the time average and τ the delay time. We consider the case where

the atom-position distribution is random and the atom number has a Poissonian

distribution. The phases of photons emitted by different atoms are random and the

total fluorescence field can be written as the sum of the fields emitted by individual

atoms. For simplicity, we consider a single polarization of the guided field. The firstand

second-order correlation (Intensity correlations) functions for nanofiber singlemode

observation have the forms [43, 44, 96]

〈E ⋆ (t)E(t + τ)〉 = I√ µ

µ o

g (1) (τ)e −iω 0τ ,

〈I(t)I(t + τ)〉 = I2

n 2 µ 0

{

ng (2) (τ)+n 2[ µ 0 + µ|g (1) (τ)| 2]} , (3.3)

where I is the intensity of the fluorescence field emitted by all the atoms combined.

g (1) (τ) and g (2) (τ) are the normalized first- and second-order correlation functions for

a single atom and n is the mean atom number. The detailed expressions for g (1) (τ)

and g (2) (τ) are given in Appendix A. Figure 3.4(a) shows the theoretical plot of

the second order correlation function g (2) (τ) (red dashed curve) and the square of

the first order correlation function, |g (1) (τ)| 2 (blue solid curve). The g (2) (τ) curve

shows the antibunching behavior, whereas the |g (1) (τ)| 2 curve shows the bunching

behavior at τ = 0 [43]. The parameter ω 0 is the atomic transition frequency. The

coefficients µ 0 and µ are determined by the mode profile function of the nanofiber

guided modes and their expressions are given in Appendix A. We point out here that

the above equations reduce to free-space single-mode observations for µ 0 = 1 and

µ = 1 [1]. In the conventional photon correlation measurements, we measure the

intensity correlations 〈I(t)I(t + τ)〉 and Eq. 3.3 shows that the intensity correlation

can give a direct measure of |g (1) (τ)| when the atom number n is large enough. Figures

3.4(b)(i-iv) shows the second-order intensity correlation function 〈I(t)I(t + τ)〉 for n


3.4. LIF Emission Spectrum Measurements : Experimental Procedures 79

(a)

(b)

1.0

(i)

I(t)I(t+τ)

(1)

g (τ)

0.8

1.0

0.7

1.0

0.7

1.0

0.6

1.0

0.0

(ii)

(iii)

(iv)

(v)

Figure 3.4: Theoretical plot of (a) g (2) (τ) (dashed curve) and | g (1) (τ) | 2 (solid curve).

(b) 〈I(t)I(t+τ)〉 for (i) n=5 atoms. (ii) 15 atoms. (iii) 25 atoms. and (iv) 100 atoms.

(v) g (1) (τ).


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 80

atoms with atom number, n = 5, 15, 25, 100 respectively. Figure 3.4(b)(v) shows

the first-order correlation function g (1) (τ) for a single-atom. The plot shows that for

the case, when the number of atoms are small, the antibunching behavior of g (2) (τ)

dominates the bunching behavior of g (1) (τ), and with an increase in the atom number

the bunching behavior of the g (1) (τ) function dominates the g (2) (τ) function. So in

our present case, where the number of atoms is small, the intensity correlation is

dominated by g (2) (τ), and the derivation of |g (1) (τ)| is not straightforward.

In some special cases it is possible to obtain g (1) (τ) from |g (1) (τ)|: for example,

when the spectrum has the Lorentzian lineshape, g (1) (τ) is derived from |g (1) (τ)| as

g (1) (τ) =|g (1) (τ)|e −iω0τ . The parameter ω 0 is the optical transition frequency. But

generally, such derivation of g (1) (τ) from |g (1) (τ)| is not always possible. In the next

section we discuss a novel method for the measurement of LIF emission spectrum. The

technique combines the optical heterodyne (OHD) technique with photon correlation

(PCR) spectroscopy.

3.4.3 Combined Heterodyne and Correlation Spectroscopy

Recently, Hong etal. has demostrated a novel method for measuring the fluorescence

spectrum of an extremely weak light source. They have combined the OHD technique

with PCR spectroscopy [95]. In this combined method, one can selectively obtain

the g (1) (τ) information from the measurement of the intensity correlations. The key

point is to mix a coherent local-oscillator (LO) light signal with the weak fluorescence

light. The observable intensity correlations can be formulated readily by replacing

the fluorescence field E(t) with E T (t) =E(t)+E LO (t) to include the LO field E LO =

|E LO |e −iωLOτ , where ω LO is the LO-frequency. The intensity correlation of the total

field E T (t) contains 16-terms. Out of this ten-terms average out to zero and the rest

six-terms appear as shown below

〈I T (t)I T (t+τ)〉 = 〈I(t)I(t+τ)〉+I LO

[

〈E ⋆ (t)E(t+τ)〉e iω LOτ +c.c. ] +2I LO I+I 2 LO . (3.4)


3.4. LIF Emission Spectrum Measurements : Experimental Procedures 81

where I LO is the intensity of the LO-light. When we insert Eq. 3.3 into Eq. 3.4,

we obtain

〈I T (t)I T (t + τ)〉 = I2

n 2 µ 0

{ng (2) (τ)+n 2[ µ 0 + µ|g (1) (τ)| 2] }

+I LO I√ µ

µ o

[

g (1) (τ)e −i(ω 0−ω LO )τ +c.c. ] +2I LO I + I 2 LO. (3.5)

We note that in terms of the fluorescence spectral density S(ω), which is given by

Eq. 3.2, expression (3.4) for the second-order correlation function 〈I(t)I(t + τ)〉 can

be rewritten as

〈I T (t)I T (t + τ)〉 = 〈I(t)I(t + τ)〉 + I LO

[ 1



∫ ∞

−∞

S(ω ′ + ω LO )e −iω′τ dω ′ +c.c. ]

+2I LO I + I 2 LO . (3.6)

Equation 3.6 shows that the second term which contains the fluorescence spectrum

S(ω) information is down-shifted by ω LO in the frequency domain. The shifted

spectrum appears around the frequency ω O − ω LO . So, we can obtain the spectral

density S(ω) by taking the Fourier transform of the correlation signal 〈I T (t)I T (t+τ)〉.

The LO frequency ω LO should be chosen such that there is no overlap between the

second term and the other terms of Eq. 3.6 in the frequency domain and also such

that the shifted spectrum frequency falls within the measurable bandwidth of the

detector.

We briefly discuss here the emission spectrum of a two-level atom at rest when

excited by a near resonant monochromatic light. The spectrum which is now widely

accepted was first calculated by Mollow [97], and one of the first experiments to

measure such fluorescence spectrum was performed by Ezekiel group [98]. Mollow

showed that the scattered light consists of both the elastic Rayleigh scattering and

the inelastic fluorescence scattering. If the excitation light intensity is greater than

the saturation intensity of the atom, the fluorescence scattering part dominates. In


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 82

the present work, we are investigating the fluorescence scattering and hence excitation

intensity has been kept high such that the Rabi frequency is greater than the natural

linewidth. Under such condition, the spectrum is given by the following equation,

S(ω) =2πA 2 δ(ω − ω L )+B ΓΩ2

Ω 4 eff

Ω 2 /2

{

(ω − ω L ) 2 + S0

2

+[ 3Ω2

8 + ∆2

4 ][ 1

(ω − ω L − Ω eff ) 2 + σ + 1

2 (ω − ω L +Ω eff ) 2 + σ2]} (3.7)

where ω L is the excitation laser frequency, Ω is the Rabi frequency, ∆ = ω L − ω 0

is the detuning of the excitation laser from the atomic transition frequency. Ω eff =


Ω2 +∆ 2 is the effective Rabi frequency. The parameters A, B, S 0 , and σ are defined

as follows,

A = Ω2 /4[∆ 2 +Γ 2 /4]

Ω 2 /2+∆ 2 +Γ 2 /4 , B = Ω 2 /4

Ω 2 /2+∆ 2 +Γ 2 /4

S 0 = Γ/2(Ω2 +2∆ 2 )

, σ = Γ(3Ω2 /4+∆ 2 /2)

Ω 2 +∆ 2 Ω 2 +∆ 2

The first term shown in Eq. 3.7 is due to the elastic Rayleigh scattering and the

rest of the terms are due to fluorescence scattering. The fluorescence scattering part

consists of three Lorentzians, one centered at the excitation laser frequency ω L , and

other two are separated from the central one by the effective Rabi frequency, Ω eff .

Figure 3.5 shows the plot of the calculated spectrum for both on-resonant and offresonant

excitations. Figure 3.5(a) shows the spectra for on-resonant excitation and

for two different Rabi-frequencies, chosen similar to our experimental parameters. The

almost single peak spectrum transits to a three-peak spectrum (Mollow-triplet) with

increase in the Rabi frequency. The side peaks are separated from the central peak

by the Rabi frequency, Ω. Figure 3.5(b) shows the spectra for off-resonant excitations

for three different detunings (∆) of the excitation laser. The Mollow-triplet spectra

can be seen for all the three detunings. The central peak is shifted from the atomic

resonance by the respective detunings. Also, the central peak height with respect to


3.4. LIF Emission Spectrum Measurements : Experimental Procedures 83

the side-peak becomes smaller with increase in the detunings. The side peaks are

separated from the central peak by the effective Rabi frequency, Ω eff . In the next

paragraph, we discuss the experiments.

The schematic diagram of the experimental setup is shown in Fig. 3.6. The

fluorescence measurements are carried out in the same manner as discussed in the

earlier section. The timing sequence used, is as discussed in Sec. 3.2. The excitation

beam, derived from EL2 laser discussed earlier, is elliptically focused to the nanofiber

with a waist size of 1 mm along the fiber axis and 0.5 mm perpendicular to the fiber

axis. The excitation beam is linearly polarized with polarization axis perpendicular

to the fiber axis. Part of the fluorescence light from atoms around the nanofiber is

coupled in the guided-modes of the nanofiber and propagates through the signal fiberline

via the tapered region. The fluorescence light is detected using single-photoncounting

avalanche-photodiodes D1, and D2 (APD, PerkinElmer SPCM-AQR/FC).

The excitation beam is frequency up-shifted by 80 MHz using an AOM (Fig. 3.6).

As discussed earlier, the frequency of the excitation beam can be varied around the

closed cycle transition of Cs D2 line, 6S 1/2 F =4↔ 6P 3/2 F ′ = 5, by tuning the RFfrequency

generator. The intensity fluctuation of the excitation laser is less than 2%.

Part of the excitation laser output is fiber-coupled to the signal fiber-line, as shown

in Fig. 3.6, and is used as the LO-light. Thus, the fluorescence spectrum frequency

falls in the frequency range around 80 MHz (=ω 0 −ω LO ). The fiber coupler mixes the

fluoerscence signal and the LO signal in 90:10 ratio respectively, to collect almost the

total fluorescence signal during mixing. The fiber coupler is built from single-mode

optical fibers, prepared using the same fiber coupler machine used for fabrication of

the nanofiber.

Photon correlation measurements are performed using the conventional HBT

setup. Photons at one end of the signal fiber-line, consisting of both atomic fluorescence

and LO light, are split into two using a 50:50 non-polarizing beam splitter

(NPBS), and are detected by two APDs, D1 and D2. The LO power (∼200 fW) has

been kept low to avoid the saturation of the APDs. Arrival times of all the photons

are recorded using a time-correlated photon-counter (PicoHarp 300, PicoQuant


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 84

(a)

Rabi-Frequency, Ω

10 MHz

24 MHz

-50 -25 0 25 50

Frequency, MHz

(b)

-15 MHz

Ω= 18 MHz

-6 MHz

∆=-15 MHz

∆=-6 MHz

+15 MHz

∆=+15 MHz

-50 -25 0 25 50

Frequency, MHz

Figure 3.5: (a) Theoretical plot of on-resonance fluorescence emission spectra of a twolevel

atom. The red-dashed and blue-solid curves are calculated for Rabi-frequencies,

Ω= 10 MHz and 24 MHz respectively. (b) Plot of off-resonant fluorescence emission

spectra for three different detunings (∆) of the excitation laser as shown in the figure.

The Rabi-frequency used for the plots are 18 MHz. The elastic Rayleigh scattering

peak has not been plotted.


3.4. LIF Emission Spectrum Measurements : Experimental Procedures 85

Cold Cs atoms

Fluorescence

Photons

Nanofiber

NPBS

M

Excitation

Laser EL2

M

B.S.

MOT Signal

Excitation beam

AOM

+80ΜΗz

L

M

LO

FC

Fiber

coupler

FC

D

2

D

1

Correlator

∆ = + 15 ΜΗz

F’ = 5


∆ = 0 ΜΗz

∆ = − 6 ΜΗz

∆ = −15 ΜΗz

F = 4

Figure 3.6: Schematic of the experimental setup for LIF emission spectrum measurements.

Fluorescence photons emitted in the guided-modes of the nanofiber are

detected at the ends of the single-mode optical fiber. MOT: magneto-optical trap,

ECDL: external cavity diode laser, B.S.: beam splitter, L: lens, AOM: acousto-optic

modulator, M: mirror, NPBS: 50:50 non-polarizing beam splitter, FC: fiber coupler,

LO: local oscillator, D1, D2: avalanche photodiodes (APD). The excitation laser

frequencies used for exciting the atoms for emission spectra measurements are also

shown.


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 86

GmbH) during each observation period of 10 µs with a resolution of 1 ns. The signals

are accumulated for 3 minutes, which requires a total experiment time of 1 hour.

Photon correlations are derived by analyzing the recorded arrival times.

Regarding the spectral resolution of the present nanofiber system, OHD-part and

PCR-part have their own limitation. Spectral resolution of the OHD-part is limited

by the accuracy of the AOM-frequency, which is about 10 kHz. On the other hand,

the resolution of the PCR-part is determined by the correlation time. In the present

system, the correlation time is effectively limited by the dwell-time of the cold-atoms

around the nanofiber. As shown in Fig. 3.3(c), the dwell time of the atoms is ∼2

µs, which corresponds to a spectral resolution of around 250 kHz. Thus, the spectral

resolution of the whole system is estimated to be 250 kHz.

3.5 LIF Emission Spectrum Measurements : Results

3.5.1 On-Resonant Excitations

We first show the LIF emission spectrum for the case where the excitation laser is

resonant to the transition 6S 1/2 F =4→ 6P 3/2 F ′ = 5, as shown by marker arrow (c)

in Fig. 3.2(b). Figures 3.7(a) and (c) show the normalized coincidences measured for

two excitation beam intensities 30 mW/cm 2 and 153 mW/cm 2 respectively, for time

delay τ = ±2 µs. Figures 3.7(b) and (d) show the enlarged view of the center region

of Figs. 3.7(a) and (c) respectively, for τ = ±100 ns.

The bunching effect of g (1) (τ) is clearly seen at zero time delay (τ = 0) in Figs.

3.7(a) and (c). In Figs. 3.7(b) and (d), one can readily recognize the oscillations with

a period of around 12 ns which reflects the difference frequency of ∼ 80 MHz between

the fluorescence frequency and the LO frequency. Envelope of the oscillation is mainly

given by the first-order correlation function as shown in Eq. 3.5. By comparing Figs.

3.7(b) and (d), one can see that at low excitation intensity, the envelope which peaks

at τ =0 falls-off smoothly, whereas Fig. 3.7(d), at high excitation intensity shows a


3.5. LIF Emission Spectrum Measurements : Results 87

(a)

(b)

12 ns

(c)

(d)

Figure 3.7: One-end photon correlation measurements with OHD technique. (a) and

(c) show the measured normalized photon correlations between photons coming into

one-end of the signal fiber-line for excitation beam intensity 30 mW/cm 2 and 153

mW/cm 2 respectively. (b) and (d) are the enlarged view of the central part of Figs.

(a) and (c) respectively. The time-period of the oscillations is shown in Fig. 3.6 (b).


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 88

dip at around τ =±25 ns.

The Fourier transform of the correlation signals shown in Fig. 3.7 will give the

emission spectrum. Figures 3.8(a) and (b) show the Fourier transform spectra (gray

curves) for Figs. 3.7(a) and (c) respectively, for frequency range from -50 to +50 MHz.

The spectrum appears around the frequency of 80 MHz, which has been shifted to

0 MHz in the plot for convenience. The spectrum in Fig. 3.8(a) shows a broader

structure than the natural linewidth with shoulders appearing on both sides of the

central-peak at around ±10 MHz. The spectrum in Fig. 3.8(b) shows a symmetric

three-peak structure. It consists of a central-peak and two smaller side-peaks separated

by around ±24 MHz from the central-peak. Also in both the spectra in Figs.

3.8(a) and (b), there is another sharp-peak on top of the central-peak. The width of

the sharp-peak is around 250 kHz FWHM, which is limited by the measurement resolution.

We measured the emission spectrum without the MOT-atoms and obtained

almost the same sharp-peak as those with atoms.

The spectra are fitted using Eq. 3.7, for fluorescence spectrum of free atoms

[97, 98]. Fitted results are plotted by black curves. Rabi-frequency (Ω) is the only

fitting parameter. The best fit for the data shown in Figs. 3.8 (a) and (b), has been

obtained for Rabi frequencies, Ω = 9.9 MHz and 24.5 MHz respectively. In Fig. 3.8

(b), the central-peak has a width of 5.8 MHz and a height 3.5 times that of the sidepeaks.

The side-peaks are located at ± 24.5 MHz from the central-peak and have

widths of about 9 MHz.

3.5.2 Off-Resonant Excitations

Next we show the emission spectrum when the excitation laser is detuned from the

atomic resonance, as shown by marker arrow (a), (b) and (d) in Fig. 3.2(b) and

also in Fig. 3.6. The excitation intensity has been kept fixed at 153 mW/cm 2 .

Figure 3.9 shows the measured emission spectra for three different excitation laser

detunings. Results are plotted by gray curves. The spectra for off-resonant excitations

are found to be shifted from the resonant case (solid vertical line shown in Fig. 3.9)

by the respective excitation beam detunings. In the observed spectra, the central-


3.6. Discussion 89

(a)

(b)

24 MHz

Figure 3.8: On-resonance fluorescence emission spectra. The gray curves in Figs.

(a) and (b) show the Fourier spectrum for the data shown in Figs. 3.6 (a) and (c)

respectively. The black curves are the theoretical fittings.

peak appears at the excitation frequency and the separation between the side-peaks

and the central-peak increases with increase in detuning of the excitation laser (∆).

This is due to the increase in the effective Rabi-frequency, Ω eff = √ Ω 2 +∆ 2 with

detuning. Also, with increase in detuning, the height of the central-peak decreases

with respect to the side-peaks. To see this effect, the vertical-axis scale has been

kept identical for all the plots in Fig. 3.9. The positive and negative side-peaks for

all the spectra observed were found to be symmetric. The signal-to-noise ratio of

the observed spectrum decreases with increase in detunings. This is because with

increase in detunings, the fluorescence photon count reduces. Measured spectra were

fitted by adjusting the Rabi frequency (Ω) [97, 98]. The best fitting was obtained

for a Rabi-frequency of Ω = 18, 16.5, and 15.5 MHz for Figs. 3.9(a), (b), and (c)

respectively. Fitted results are plotted by black curves.

3.6 Discussion

We have measured both the LIF excitation and emission spectrum for atoms around

the nanofiber, the average number of which is about fourteen. The emission spectrum

measurements were done by integrating the fluorescence photons for a time of 3


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 90

(a)

Spectral density, [a.u.]

(b)

(c)

+ +

Figure 3.9: Off-resonant fluorescence emission spectra for different excitation beam

detunings. The gray curves are the measured spectra and the black curves are the

theoretical fitting. The spectra have been measured for a detuning of (a) -15 MHz,

(b) -6 MHz, and (c) +15 MHz. The solid red line is a reference to show the relative

shift of the spectrum for detuned excitations with respect to the resonant excitation.


3.6. Discussion 91

minutes, which is much less than the time required for free-space measurements (∼1

hour) [22]. The present high sensitivity is due to the efficient collection of few-atom

fluorescence in single-spatial mode through the guided-modes of the nanofiber and

the photon-counting based measurements.

In the present work, the excitation beam intensity has been kept much higher

than the saturation intensity of the Cs atoms, to investigate the inelastic scattering

part of the fluorescence emission spectrum which is distributed in a frequency range

broader than the natural linewidth. As exhibited in Figs. 3.8 and 3.9, each of the

spectra reveals a broad structure, consisting of a central-peak along with the two

side-peaks and a sharp-peak on the central-peak. The three-peak structure is well

explained by the theoretically calculated Mollow-triplet spectrum for free atoms, and

the sharp-peak is assigned to the elastic scattering. We mention here that although

the details of the spectrum depend on the multi-level structure of the Cs atom [35, 61],

the underlying physics can still be explained in the framework of the two-level atom

model. We note here that the Rabi-frequency, calculated from the experimentally

measured excitation beam intensity is found to be larger than that obtained from the

theoretical fitting, and differs by a factor of around 1.5 to 2. This difference might be

due to the position distribution of MOT atoms with respect to the intensity profile

of the excitation beam, along the axis of the nanofiber. Also, due to some residual

magnetic field in the MOT region the dipole moment orientation of the atoms will

have some distribution which may contribute to such deviations in the observed Rabifrequency.

Regarding the sharp-peak due to the elastic scattering, it is understood as scattering

from silica nanofiber, since it is observed without atoms. Elastic Rayleigh

scatterings from atoms may be included in the sharp peak, but the contribution from

the Cs atoms should be much smaller than the bulk-silica nanofiber scatterings.

We did not see any significant difference from the free-atom theory, although

some signatures of the vdW interaction is observed in the red-side of the excitation

spectrum. It means that the effect of the vdW interaction on the emission spectrum

is still small compared to the free-atom contribution under the present conditions.


Chapter 3. Fluorescence Spectrum of Strongly Driven Atoms 92

Although some surface effects might be included in the emission spectrum, but with

the present signal-to-noise ratio we could not observe any difference between the

positive and negative detuning. We note that the signal-to-noise ratio of the present

measurements can be increased by improving the transmission of the fluorescence

photons through the signal fiber-line.

The experiments described in this chapter have been carried out under the freeatom

conditions with the use of an additional irradation of UV laser. It would be

meaningful to extend the present method to a situation where atom-surface interaction

is enhanced. Specifically the interaction of atoms with the surface leads to

many vibrational levels [61], and therefore the spectrum of atom with those vibrational

levels will be broad and the three-peak structure should no longer be visible

in the emission spectrum. Such measurements may give a novel tool to clarify the

mechanism of atom-surface interactions.

Finally, we should mention a possible extension of the present method to the

dipole-trapped atoms around nanofiber. Recently, a realistic dipole-trapping scheme

has been discussed theoretically [34], and has been demonstrated experimentally [46].

By incorporating such dipole-trapping scheme, the present method may be used to

study atom dynamics in the trap potential.

3.7 Conclusions

We show that LIF excitation and emission spectra of a small number of strongly driven

cold atoms can be investigated using optical nanofibers. This is because, atoms which

lie in the vicinity of the optical nanofiber can emit a significant fraction of fluorescence

photons in the single-guided-modes of the nanofiber (∼2 %). We have measured the

fluorescence spectrum of approximately fourteen Cs atoms around a nanofiber. For

the emission spectrum measurements, the optical nanofiber method is combined with

OHD technique and PCR spectroscopy. The combined method is used for the first

time for fluorescence emission spectrum measurements. The spectral resolution in the

present emission spectrum measurements is ∼250 kHz and is limited by the dwell-time


3.7. Conclusions 93

of atoms around the nanofiber and the measured correlation time. The observation

of Mollow-triplet in the emission spectra, even though a slight red-tail is observed in

the excitation spectra, confirms the free-space two-level atom behavior of near surface

atoms. The realization of free-atoms near such nanofiber can be used for control and

manipulation of atoms without the dephasing effects of surface potential. The present

method of LIF measurements using nanofiber, in addition to the combined OHD and

PCR technique, may give a new tool for investigating atom fluorescence, not only

for free-atoms but also for atoms in various boundary conditions, such as atoms near

some interface or dynamics of atoms trapped in an optical dipole potential.


chapter 4

PROBING ATOM-SURFACE INTERACTIONS USING

OPTICAL NANOFIBERS

4.1 Introduction

The atoms emitting fluorescence in the guided-modes of the nanofiber lie very close

to the nanofiber surface. Due to this close proximity, atoms are subjected to atomsurface

interactions. Now as mentioned in Chap. 1, signatures of atom-surface interaction

in the form of a large tail in the red-detuned side (red-tail) have been observed

in the LIF excitation spectrum of atoms around the nanofiber [40]. The lineshape of

the excitation spectrum is understood as a result of a process where atoms approaching

the nanofiber surface fall into the local surface potential, forming long-range

atom-surface bound states. Also it has been reported that such spectrum lineshape

changes with the application of an external UV laser [41, 42]. In the experiments

described in Refs. [41, 42], it has been found that the long tail appearing in the reddetuned

side of the spectrum due to surface-interaction vanishes with the irradiation

of the MOT-atoms with an UV laser (407 nm) and the spectrum shape evolves to an

96


4.2. LIF Spectrum Measurements of Surface-Bound Atoms: Experimental Procedures 97

almost free-atom like Lorentzian spectrum. In this chapter, we extend the previous

works and investigate the evolution of the lineshape of the excitation spectrum from

a Lorentzian to broad red-tail condition. We also investigate the emission spectrum

under such broad red-tail conditions.

4.2 LIF Spectrum Measurements of Surface-Bound

Atoms: Experimental Procedures

The conceptual diagram of the experimental setup is shown in Fig. 4.1. As discussed

in Chap. 3, the experiments are performed by overlapping cold Cs-atoms with an optical

nanofiber and detecting the fluorescence photons emitted in the guided-modes of

the nanofiber. The timing sequence for all the measurements is identical to that described

in Chap. 3. The excitation spectrum is measured by scanning the excitation

laser frequency around the transition 6S 1/2 F =4→ 6P 3/2 F ′ = 5 and measuring the

fluorescence coupled in one-end of the guided-modes of the nanofiber. For the emission

spectrum measurements we combine the optical heterodyne technique with the

photon-correlation spectroscopy, as discussed in Chap. 3. The frequency difference

between the local oscillator and the excitation beam has been increased from 80 MHz

to 130 MHz, in anticipation of a wide-bandwidth spectrum of atoms experiencing

surface interactions. So, the difference frequency between the fluorescence photons

and the LO will appear around 130 MHz.

For the nanofiber surface manipulation, a separate UV laser has been used as

discussed in Ref. [42]. The UV laser beam is a free-running 407 nm laser, aligned

collinear with the excitation beam and its size at the position of the MOT atoms

is 2 mm. The excitation beam and UV laser beam are irradiated perpendicular to

the nanofiber. Also as mentioned before, the background Cs-atom density also plays

a crucial role in manipulating the surface conditions [41]. The background Cs-atom

flux and hence the density can be controlled in a reproducible way by changing the

Cs-atom dispenser current (I d ) [99]. The Cs-atom dispenser is a resistively heated


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 98

Cs atoms in MOT

Nanofiber

Excitation laser

Fluorescence

UV laser

Figure 4.1: Conceptual diagram of the experimental setup. The nanofiber is located

at the waist of a tapered optical fiber. Fluorescence photons emitted in the guidedmodes

of the nanofiber are detected at the ends of the single mode optical fiber. The

UV laser and the excitation laser are alligned collinear to each other.

alkali metal dispenser source (SAES Getters) installed inside the vacuum chamber

to generate Cs-atoms for the MOT [100]. The dispenser atom source consists of Cschromate

salt (Cs 2 CrO 4 ) with a reducing agent (St 101) and is packed in a trapezoidal

housing. The dispenser source is controlled by a DC current provided through two

electrical feed throughs into the chamber and the ohmic heating of the dispenser starts

the reduction process of the salt. The reducing agent also sorbs any contaminants

released during the reaction other than the Cs atoms. To make sure that the heating

process as well as the reducing agent itself does not release any unwanted particles

during the reaction, the dispenser is baked up to maximum current of 5.2 A for more

than 12 hours before starting the experiments. The generation rate of Cs atoms is

highly reproducible. The dispenser is kept at a distance of 5 cm from the nanofiber.

It has been found that the rate at which the excitation spectrum lineshape changes

depends on the Cs dispenser current (I d ). The more the I d , the faster is the change

in the shape of the spectrum. In the next section, we discuss the LIF spectrum

measurements.


4.3. LIF Spectrum Measurements of Surface-Bound Atoms: Results 99

4.3 LIF Spectrum Measurements of Surface-Bound

Atoms: Results

In this section, we systematically investigate the fluorescence spectrum of atoms

around the nanofiber under various nanofiber surface conditions. The surface conditions

are manipulated by the use of UV lasers and by controlling the Cs-atom

dispenser current, as mentioned earlier. Under this modified surface conditions, we

have investigated both the LIF excitation and emission spectrum of atoms.

4.3.1 LIF Excitation Spectrum Measurements: Experimental

Preparations and Results

We have carried out the excitation spectrum measurements for a dispenser current

(I d ) of 5.2 A, to keep the same experimental condition regarding atom number as for

experiments described in Chap. 3. The MOT is overlapped with the nanofiber and is

first irradiated with a UV laser (407 nm) for about 5 minutes. The UV laser intensity

is 220 mW/cm 2 . Figures 4.2(A-D) shows the excitation spectra measured just after

switching off the UV light. The excitation laser beam intensity is 0.7 mW/cm 2 at

the position of the MOT-atoms. The fluorescence coupled in one-direction of the

nanofiber is detected by an APD and the photon counts are then recorded by a

photon counting board. The spectra A, B, C, and D are measured one after another

consecutively and the measurement time for each spectrum is around 6.5 minutes. The

plots show the normalized photon counts to see clearly the change in the lineshape of

the excitation spectrum. The absolute photon counts can be derived from the scaling

factors shown in the plots.

The spectrum A which is measured just after switching off the UV laser, has its

peak at the resonance and a very small tail on the red-detuned side. The spectrum

B, which is measured 6.5 minutes after spectrum A, has its peak at resonance but

the small red-tail now becomes prominent and extends up to -80 MHz. Also, there

is a decrease in the peak photon-counts. With time, the red-tail becomes broader


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 100

A

B

Normalized photon counts

C

D

-120 -90 -60 -30 0 30

Excitation laser detuning (∆), MHz

Figure 4.2: Measured fluorescence excitation spectra. The spectrum A is measured

just after irradiating the UV laser. Spectra B, C, and D are measured one after

another consecutively and the measurement time for each spectrum is around 6.5

minutes. The scaling factors are shown in the figure.The spectra are background

corrected.


4.3. LIF Spectrum Measurements of Surface-Bound Atoms: Results 101

and extends till -100 MHz, and the peak appearing at the resonance reduces further

(spectrum C). Finally, there starts appearing two-peaks in the spectrum (spectrum

D). One of the peaks which is sharp appears at the resonance and other peak which

is broad appears around a detuning of ∆= -70 MHz ∼ -90 MHz.

The FWHM of the spectrum A, B, and C are 10 MHz, 12.5 MHz and 25.4 MHz

respectively. In spectrum D, the peak which appears at the resonance has a very small

red-tail and the FWHM is around 11.5 MHz. The other peak which appears around

∆ = -70 MHz ∼ -90 MHz has a long red-tail extending beyond -120 MHz. We have

found that with the irradiation of MOT-atoms by the UV laser under the condition

of spectrum shown in D, the excitation spectrum lineshape again returns back to that

of the spectrum shown in A, with the on-resonant fluorescence counts return back to

the same fluorescence intensity. We should mention here that irradiation of UV beam

in the absence of MOT atoms has no effect on the excitation spectrum.

4.3.2 Effect of UV laser irradiation

To investigate the changes in the spectral shape shown in Figs. 4.2(A-D), we have

systematically measured the dependence of on-resonant (∆=0) fluorescence counts

on various irradiation conditions of UV laser. The excitation laser intensity is kept

at 7 mW/cm 2 . The UV laser intensity is kept at 150 mW/cm 2 and the dispenser

current is I d = 5.2 A. Figure 4.3(a) shows the observations. The observed scattering

background is 5 × 10 4 counts/s (marked as level B in Fig. 4.3(a)). Then the MOT B-

field is switched on for some time (marked as (i) in Fig. 4.3(a)) and the photon counts

increases to 8.5 × 10 4 counts/s due to the fluorescence from MOT-atoms. Then the

MOT B-field is switched off, the count decreases to background level B. The UV

laser is then switched on for some time (marked as (ii) in Fig. 4.3(a)). Under this

condition there is no MOT and the photon counts increase to 6.5 × 10 4 counts/s due

to scattering from the UV laser. Then the UV laser is switched off and the counts

decreases to background level B. Then again the MOT B-field is switched on (marked

as (iii) in Fig. 4.3(a)). The photon count increases due to the fluorescence, however

there is no observable change in the fluorescence level. Hence it is clear from the


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 102

(a)

Counts / s

1.6x10 6 S2

1.2x10 6

S1

8.0x10 5

4.0x10 5

8.0x10 4

4.0x10 4

(i)

(ii)

B B B

(iii)

(iv)

(v)

UV

Laser

0.0

0 500 1000

MOT

B-field

OFF

ON

ON

OFF

OFF

ON

ON

OFF

(s)

(b)

Counts /s (x 10 5 )

20

16

12

8

4

S1

S2

0

0 100 200 300 400 500 600

UV laser Intensity (mW/cm 2 )

Figure 4.3: (a) Measured on-resonant fluorescence for various irradiation conditions

of UV laser. The timing sequence used for the UV laser and MOT B-field is shown

below. (b) The dependence of the S1 (square-solid line, black curve) and S2 (circlesolid

line, red curve) count levels on the intensity of UV laser.


4.3. LIF Spectrum Measurements of Surface-Bound Atoms: Results 103

observations that the irradiation of UV laser in the absence of the MOT has no effect

on the observed fluorescence counts. Next we switch on the UV laser for some time

in the presence of MOT (marked as (iv) in Fig. 4.3(a)). Switching on the UV laser in

presence of MOT, the photon count increases drastically upto a level S1 (1.1 × 10 6

counts/s) and the increase in the counts is due to the increased fluorescence level as

scattering counts from the UV laser is almost negligible. The observation shows that

irradiation of MOT-atoms by the UV laser has dramatic effect on the fluorescence

level. Finally we switch off the UV laser (marked as (v) in Fig. 4.3(a)). By switching

off the UV laser the fluorescence counts further increases to a level S2 (1.5 × 10 6

counts/s) and then slowly decays in time.

We have extended the above measurements for different UV laser intensities. In

Fig. 4.3(b), we plot the levels S1 and S2 for different intensities of the UV laser.

It is clear from the plot that the level S1 (during which UV laser is ON) decreases

with increasing the UV laser intensity whereas the level S2 (UV laser off) is almost

constant.

4.3.3 Hot atom effect on the surface

As shown in Figs. 4.2(A-D), the change in the lineshape of the excitation spectrum

is characterized by the appearance of a red-tail and a decrease in the on-resonant

fluorescence counts with time. To investigate such changes in the excitation spectrum

lineshape, we have measured the time-dependence of the on-resonant fluorescence

(level S2, as shown in Fig. 4.3(a)), for three different dispenser currents (I d ). The I d

controls the flux of Cs-atoms in the vacuum chamber, as mentioned earlier [84]. The

UV laser intensity is kept at 150 mW/cm 2 .

Figure 4.4 shows the time-dependence of the on-resonant fluorescence for three

different dispenser currents. For each measurement the MOT, overlapped with the

nanofiber, is first irradiated with the UV laser for about 5 minutes and the observations

are carried out after switching off the UV laser. The observed initial fluorescence

count depends on the atom density around the nanofiber and therefore is high for

higher dispenser current. One can see that for a dispenser current of I d = 4.8 A (Fig.


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 104

Figure 4.4: Time dependence of the on-resonant fluorescence as a function of the

dispenser current, I d . (a) for I d = 4.8 A (black curve). (b) for I d = 5.2 A (green

curve). (c) for I d = 5.6 A (red curve). Each measurement is carried out just after

switching off the UV laser. For the measurement shown in (b), for I d = 5.2 A,

the MOT is switched-off between 750 s to 800 s and the photon counts drop to the

scattering background level and recovers to the same decay trajectory.


4.3. LIF Spectrum Measurements of Surface-Bound Atoms: Results 105

4.4(a)), the initial photon counts of 3.3 × 10 5 counts/s, decreases slightly within a

time period of 3000 s. As we increase the dispenser current to I d = 5.2 A (Fig. 4.4(b)),

the initial counts of 8.2 × 10 5 counts/s decreases with the decay time of ∼900 s. With

further increase in I d to 5.6 A (Fig. 4.4(c)), the initial photon counts of 10.2 × 10 5

counts/s decreases rapidly with a decay time of ∼47 s. The observations show that

continuous use of high dispenser current changes the on-resonant fluorescence. The

temporal behavior of the decay of on-resonant fluorescence for I d = 5.2 A shown in

Fig. 4.4(b), can explain the evolution of the lineshape of the excitation spectra shown

in Figs. 4.2(A-D). During the measurement of fluorescence for I d = 5.2 A, we have

switched off the MOT (MOT B-field and lasers are off, dispenser is on) for a period

of 50 s from 750 s to 800 s. As shown in Fig. 4.4(b), we have found that fluorescence

counts suddenly drops to the scattering background level and recovers to the same

decay trajectory.

The realization of a stable lineshape of the excitation spectrum, with a steady

fluorescence counts for any excitation laser frequency, is important for quantitative

experiments, especially for experiments like emission spectrum measurements, where

long data integration time of ∼1 hour is required to have a good signal-to-noise ratio.

The lineshape of the excitation spectrum can be maintained for low dispenser currents,

as shown by the almost steady on-resonant fluorescence counts for I d = 4.8 A in Fig.

4.4(a), but the initial photon counts is ∼3 times smaller compared to that at higher

dispenser current of I d = 5.6 A (Fig. 4.4(c)). A high photon count rate is important

to achieve a good signal-to-noise ratio in the experiments. We have found that, if

we keep the UV laser on during the measurements with very low intensity of 5A.


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 106

Figure 4.5: Spectrum C shown in Fig. 4.2 (square dot), along with a Lorentz curve

(solid line). The spectrum is background corrected.The two arrows correspond to the

detunings, ∆= -20 MHz and +20 MHz, for which the emission spectra have been

investigated.

4.3.4 LIF Emission Spectrum Measurements : Experimental

Preparations and Results

To further clarify the behavior of atoms near the surface, we have measured the

emission spectrum for the condition when a large red-tail is observed in the excitation

spectrum. Under the conditions of the excitation spectra shown in Figs. 4.2(A-B),

the emission spectra can be explained by the free-atoms Mollow-triplet spectra, as

shown in Chap. 3. In this section, we show the emission spectrum measured under

the condition corresponding to that shown in Fig. 4.2(C) at I d = 5.2 A. Figure 4.5

shows spectrum C along with a Lorentz curve, to clearly see the difference of the

observed spectrum from the atomic Lorentzian shape in the red-detuned side of the

spectrum. The Lorentz curve has been obtained by fitting the observed spectrum

from the central part to the blue-detuned part of the spectrum. The FWHM of the

Lorentz curve is 10.2 MHz. The UV laser is continuously irradiated, with a very small

intensity of 0.5 mW/cm 2 . Under these conditions, the spectrum lineshape shown in

Fig. 4.5 can be kept constant for more than 1 hour.


4.3. LIF Spectrum Measurements of Surface-Bound Atoms: Results 107

(a)

∆ = + 20 MHz

(c)

(b)

∆ = - 20 MHz

(d)

7.5 ns

Figure 4.6: One-end photon correlation measurements with heterodyne technique.

Measured normalized photon correlations between photons coming in one-end of the

nanofiber for time delay ±2 µs, for (a) +20 MHz detuned excitation. (b) -20 MHz

detuned excitation. (c) and (d) are the enlarged view of (a) and (b) respectively, for

time delay ±100 ns. The measurement resolution is 0.5 ns.


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 108

The emission spectrum measurements have been carried out for two detunings

(∆) of the excitation laser (as shown by arrow markers in Fig. 4.5) and the excitation

laser beam intensity has been kept at 153 mW/cm 2 . Figures 4.6(a) and (b) show the

normalized coincidences for time delay ±2 µs measured for ∆= +20 MHz and ∆=

-20 MHz respectively. The time resolution is 0.5 ns. Figures 4.6(c) and (d) show the

enlarged view of Figs. 4.6(a) and (b) respectively. One can readily see the oscillations

in Figs. 4.6(c) and (d) with a time period of around 7.5 ns which corresponds to the

beat frequency of 130 MHz between the fluorescence photons and the local oscillator.

Figure 4.6(c) shows a symmetric envelope and there is a dip on both sides at around

±20 ns. In Fig. 4.6(d) the observed envelope of the oscillations is asymmetric for

positive and negative time delay. The envelope falls off smoothly on the positive side

of the delay, whereas for negative delay the envelope shows a dip at around -25 ns.

The Fourier transform spectra of the signals shown in Figs. 4.6(a) and (b) are

shown in Figs. 4.7(a) and (b) respectively. The frequency axis is with respect to

the atomic transition F =4→ F ′ = 5. Figure 4.7(a) shows the emission spectrum

for ∆ = +20 MHz excitation. It consists of three-peaks, one central-peak and two

side-peaks. The sharp elastic scattering part appears on top of the central-peak

and is shifted from the atomic resonance by +20 MHz. The observed spectrum

has been fitted with a free-atom spectrum [98] shown by the black curve in Fig.

4.7(a). The observed spectrum for ∆ = +20 MHz excitation agrees well with the

theoretical calculations for the spectrum of free-atoms. The side-peaks are separated

from the central-peak by 27 MHz, which corresponds to the effective Rabi frequency,

Ω eff

= √ Ω 2 +∆ 2 . Figure 4.7(b) shows the emission spectrum for ∆ = −20 MHz

excitation. The signal strength is 2.5 times stronger than that for ∆ = +20 MHz

as shown by the scaling factors. The observed spectrum is broad with a sharp-peak

like profile appearing on top of the broad profile. The sharp-peak is shifted from the

atomic transition by -20 MHz and is due to the elastic scattering of the bulk silica.

The width of the sharp spectrum is limited by the present measurement resolution

of ∼250 kHz, which is determined by the total correlation time 4 µs (time range

between -2µs to +2µs). The broad profile is asymmetric and extends upto +10 MHz


(

4.3. LIF Spectrum Measurements of Surface-Bound Atoms: Results 109

(a)

1

∆ = + 20 MHz

27 MHz

(

(b)

-60 -40 -20 0 20 40 60 80

2.5

∆ = - 20 MHz

-60 -40 -20 0 20 40 60 80

Figure 4.7: Fourier spectra (Gray curves) of the signals shown in Fig. 4.6, for (a) ∆ =

+20 MHz detuned excitation. (b) ∆ = -20 MHz detuned excitation. The resolution

is 250 kHz. The scaling factors are shown in the figure.The frequency axis is with

respect to the atomic transition 6S 1/2 F =4→ 6P 3/2 F ′ = 5. The black curve in Fig.

4.7(a) is the theoretical fit of the spectrum.

(

(


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 110

on the positive side and -50 MHz on the negative side. The peak of the broad profile

is shifted from the atomic transition by -30 MHz. The broad spectrum has a width

of 40 MHz which is around 8 times the natural linewidth of Cs atom (5.2 MHz).

4.4 LIF Spectrum Measurements: Analysis and

Discussions

The observed LIF excitation spectrum lineshape can be understood by considering

the center-of-mass motion of the atom in the close vicinity of nanofiber surface. The

potential energy of the atom-surface interaction is a combination of a long-range van

der Waals (vdW) attraction and a short range repulsion. The vdW attraction is

described by the potential function −C 3 /x 3 , where C 3 is the vdW coefficient. The

short-range repulsion is approximated by an exponential function Ae −αx , where the

parameters A and α determine the height and range, respectively of the repulsion

potential. The combined potential depends on the internal state of the atom and

the parameters for the potential are considered for Cs-atom D 2 line and fused silica

surface [60, 61]. A schematic diagram of the surface induced potential is shown in

Fig. 4.8(a). The depth of the surface induced ground- 6S 1/2 and excited-state 6P 3/2

potentials are 160 THz and 316 THz respectively. The excited state potential is

around twice deeper than the ground state potential and is the reason for the surface

induced red-shift in the transition frequency of the atom near the nanofiber surface.

As discussed in Refs. [20, 21], the eigenstates for the center-of-mass motion of the

atom in the surface induced potential are analogous to molecular vibrational states,

where the molecule consists of the surface and the atom. The eigenstates are the so

called atom-surface bound states.

4.4.1 Atom-Surface Bound States

A detailed theoretical analysis for the optical excitation spectrum of Cs-atoms in

the vicinity of a flat surface can be found in Refs. [60, 61]. The eigenvalues and


4.4. LIF Spectrum Measurements: Analysis and Discussions 111

wavefunctions of center-of-mass motion, the overlap integrals or the Franck-Condon

factors between the ground and excited translational levels, and the radiative decay

rates of translational levels are calculated, and the optical excitation spectrum is then

calculated following a systematic density matrix formalism. The flat-surface results

can be compared with the present experimental round-nanofiber-surface results based

on the following approximations. When the atom is close to the nanofiber surface,

the axial angular momentum is small and the effect of the centrifugal potential is

negligible compared to the vdW potential. The reflection of an incident plane wave

from a cylindrical surface is rather complicated but is negligible due to the small

reflection coefficient for a 852 nm light at silica-vacuum interface. For short distances

the effective surface felt by the atom is essentially flat and the flat-surface results are

applicable. For large distances the topology of the surface can be seen by the atom,

but at such distances the surface-induced potential is rather small. We should note

that in the vicinity of the flat-surface the spontaneous decay rates can be decomposed

into contribution from evanescent modes and radiation modes. The decay rate into

the evanescent modes is analogous to the decay rate into the guided modes in case of

nanofiber. Thus the underlying physics for the present experiments can be understood

from the flat-surface analysis.

As seen in Fig. 4.8(a), we consider two types of transitions. One is for the

transitions from free ground-states to the bound vibrational-states of the excited

vdW potential. This transition is the so called photoassociation process. The other

is for transitions from bound ground-vibrational states to bound excited-vibrationalstates

and is referred to as bound-to-bound transitions. The overlap integrals or the

Franck-Condon factors determine the transition probability between the ground and

excited translational levels. The overlap between the center-of-mass wave functions

of a bound excited-state level and a bound ground-state level is substantial only when

the corresponding turning points are close to each other. Since the vdW potential

for the excited state is deeper than that for the ground state, the frequency shifts

of the transitions that are associated with substantial Franck-Condon factors are

mostly negative. For bound-to-bound transitions, deeper ground vibrational states


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 112

(a)

Nanofiber

Surface

Atom-Surface Bound States

Excited State

(b)

Free to Bound

Transitions

Free-atom like

Lorentzian Spectrum



Bound

to

Bound

Transition

Free to Bound Transition

Photo-Association

Process

Free Atom

Ground State

Analogous

to Molecules

(c)

Bound to Bound

Transitions

Distance (x)

Figure 4.8: (a) Schematic diagram showing the bound states of atoms in the surface

induced potentials. Two types of transitions are shown. One is from free ground state

to bound excited state referred to as photoassociation process or free-to-bound transition.

The other is transition from bound ground state to bound excited state referred

as bound-to-bound transition. (b) The calculated rate, Γ (g)

sc of light scattering from

the atom in the guided-modes of a nanofiber through the free-to-bound transitions

as a function of the detuning, ∆. The atom is initially in a thermal mixture of free

ground-states with temperature T=1600 µK. (c) Rate Γ (g)

sc of light scattering from

the atom in the guided-modes of a nanofiber through the bound-to-bound transitions

as a function of the detuning (∆) of the excitation field.


4.4. LIF Spectrum Measurements: Analysis and Discussions 113

can substantially overlap with deeper excited-vibrational-states. Since the depths of

the surface induced potentials are large, the range of the frequency shifts of strong

bound-to-bound transitions is broad and the shifts can reach large negative values.

For free-to-bound transitions, the Franck-Condon factors are more substantial for

shallow bound-excited-states than for deep ones. When the temperature of the atomic

system is low, the typical energy values of the free ground states are small and the

range of the frequency shifts of strong free-to-bound transitions is small compared to

that of bound-to-bound transitions.

The rate Γ (g)

sc of light scattering from the atom in the guided-modes of a nanofiber

through the free-to-bound transitions as a function of the detuning ∆ is shown in

Fig. 4.6(b) [61]. The atom is initially in a thermal mixture of free ground states with

temperature T=1600 µK. As one can see the spectral profile is quite narrow with a

peak near the atomic resonance. The width of the spectrum is ∼ 6.7 MHz, close to

the atomic linewidth of 5.2 MHz of the D 2 -line of atomic Cesium. The spectral profile

is slightly asymmetric with a small red-tail.

Spectral profiles for bound-to-bound transitions are shown in Fig. 4.6(c). The

profiles has been calculated by assuming equal population distribution for groundvibrational-states

down to a binding energy of 1 GHz. Regarding the highest bound

ground states, vibrational states that have binding energy larger than the thermal

energy (K B T , T= 1600 µK) of the atomic cloud has been included, because atoms

in shallower bound ground state may easily escape from the potential due to their

thermal energy. The high temperature of T=1600 µK, has been chosen to reproduce

the experimental result, shown in Fig. 4.2(D). The high temperature can be explained

by taking into consideration the repeated phonon emission and absorption by bound

atoms, due to working long time with high dispenser current. This spectrum shows

a substantial negative shift of about -50 MHz for the position of the peak.

linewidth of the spectrum is more than 60 MHz, which is one order larger than the

natural linewidth of 5.2 MHz of the D 2 -line of atomic Cesium.

spectrum has a substantial long tail on the negative-side of the detuning.

The

Furthermore, the

The observed spectral profile in the experiments can be attributed to both free-


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 114

to-bound (photoassociation process) and bound-to-bound transitions. The observed

excitation spectrum A in Fig. 4.2, which has been observed just after irradiating the

MOT-atoms shows a Lorentzian like shape and may correspond to the photoassociation

process due to free-to-bound transitions, as shown by the theoretical calculation

in Fig. 4.8(b). With time the spectrum shape changes and a red tail starts appearing

in the spectrum. This red-tail can be attributed to bound-to-bound transitions as

shown by the theoretical calculation in Fig. 4.8(c). So, the spectrum B, C, and D in

Fig. 4.2 can be explained by considering both the free-to-bound transitions of freeatoms

and bound-to-bound transitions of bound-atoms in the surface potential, with

appropriate weight ratios. The weight ratio depends on the population distribution

of atoms in free- and bound-states. With time the red tail becomes prominent showing

that the bound-atoms contribution to the fluorescence becomes dominant with

respect to the free-atoms. We note here that the contribution from bound-atoms is

due to atoms bound in the shallow-surface potential. This is because for atoms bound

in deep-surface-potential, there is no contribution to the scattering in the frequency

(energy) range (∼100 MHz) of the present excitation spectrum measurements.

The observed emission spectrum shown in Fig. 4.7 shows clear evidence of bound

atoms. The emission spectrum for +20 MHz excitation shows the three-peak spectrum

(Mollow-triplet spectrum) of free-atoms, whereas spectrum for the -20 MHz

excitation shows a wide bandwidth spectrum with no clear peak like structure. The

observations suggest that by changing the excitation laser frequency, we are selectively

observing two classes of atoms. For ∆= +20 MHz excitation, both free-atoms

and bound-atoms are out of resonance, but the transition moment including Franck-

Condon factor for bound-atoms should be much weaker than that for free-atoms [61].

Hence, we are mainly observing free-atoms and the spectrum shows the three-peak

Mollow-triplet behavior. On the other hand, for ∆= -20 MHz excitation, free-atoms

are out of resonance, but the bound-to-bound transitions are still resonant. Hence,

we are mainly observing the bound-atoms. The observed broad spectrum with no

clear peak, is due to the molecular behavior of the bound-atoms. The observed signal

strength is 2.5 times stronger than that for ∆= +20 MHz excitation and the Mollow-


4.4. LIF Spectrum Measurements: Analysis and Discussions 115

triplet structure due to free-atoms is completely covered up by the broad spectrum

of the bound atoms. This is in contrast to the observations, discussed in Chap. 3,

where the emission spectra measured for both the negative- and positive-detuned

excitations, show the Mollow-triplet spectrum (Fig. 3.9) [101]. We should mention

here that for the present emission spectra measurements, the high resolution of ∼250

kHz is crucial as the spectrum of atoms is distributed within 60 MHz and cannot be

resolved by conventional techniques, like grating based spectrograph.

For the above analysis, a temperature dependent population distribution of atoms

in the ground vibrational states of the surface induced potential has been assumed.

Now the question is what is the mechanism for the initial loading of atoms in the

shallow-surface-potential. In the next section, we discuss one possible way to explain

the loading mechanism based on atom-phonon interactions.

4.4.2 Phonon-Mediated Loading in the Surface-Potential

In this section, we discuss the possibilty of phonon-mediated loading of atoms in the

shallow surface potential. The nanofiber is at room temperature (300 K), and the

thermal vibrations of the surface may modulate the wavefunction of the approaching

cold atoms. As a result atoms may loose or gain energy via phonon emission (freeto-bound

decay) or absorption (free-to-free upward decay) respectively. The phonon

absorption acts as a heating process and the phonon emission acts as a loading process

into the surface potential. A detailed theoretical analysis of phonon mediated decay

of translational levels of atoms in a surface induced potential can be found in Ref.

[102].

We should note that the phonon interaction does not change the internal state

of the atoms, the modification is only in the motional state of the atoms. Since the

atoms are initially in the free state, we consider the transitions from the free state.

The free-to-bound transitions determine the loading rate into the surface potential or

the adsorption process and the free-to-free transition determine the heating process.

The theory suggests that for a temperature range of 100 µK to 400 µK of the atoms,

the adsorption rate is about two times larger than the heating rate [102]. Hence,


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 116

(a)

(b)

(c)

(d)

Si

Si-Bulk

~ 10 nm

DOS (10 14 states wave number -1 cm -3 )

1

0.8

0.6

0.4

0.2

0

0 20 40 60 80 100

Energy (wave number)

Free-to-bound

transition rate [s -1 ]

Two-Phonon (Raman)

Scattering

Figure 4.9: (a) Theoretically calculated phonon-mediated free-to-bound decay rate

as a function of the atomic temperature T 0 in the ranges from (a) 100 µK to 400 µK

and (b) from 50 K to 350 K. The temperature of the phonon bath is T =300 K. (c)

Schematic diagram of a silica nanoparticle of diameter 10 nm attached to a silica bulk.

Also shown is the calculated local phonon-mode-density around such nanoparticle.

(d) Calculated free-to-bound transition rate as a function of the ground-bound-level

energy of the surface potential. The initial atomic temperature is 200 µK. Also

shown schematically are the transitions (arrow marks) showing two-phonon (Raman)

scattering process.


4.4. LIF Spectrum Measurements: Analysis and Discussions 117

the phonon mediated decay may qualitatively explain the loading mechanism into

the surface potential and the loss of atoms due to adsorption. However, for the

temperature range of 100 µK to 400 µK of the atoms, the theoretically estimated

free-to-bound transition rates are in the order of 10 4 s −1 as shown in Fig. 4.9(a) [102].

So the characteristic loading time into the surface potential is much longer than the

transit time of atoms and the atoms may behave as almost free atoms around the

nanofiber. The analysis suggests that if the surface of nanofiber behaves as an ideal

surface, then one can ignore the phonon interactions. But in real experiments the

surface might be modified due to some experimental conditions, and such a broad

spectrum is observed due to some modified surface conditions where the phononmediated

decay-rate and hence the loading rate into the surface potential might be

enhanced as discussed below.

As is evident from the Figs. 4.4(a)-(c), with an increase in the dispenser current,

the rate of decay of the on-resonant fluorescence signal increases. Such a decay of the

on-resonant fluorescence is a measure of the changing surface condition. We suspect

that hot atoms from the dispenser may play a major role in changing the surface

conditions of the nanofiber. The observed ∼20 times faster decay rate for I d = 5.6 A,

compared to that for I d = 5.2 A may well correspond to the exponential increase in the

flux of the background room-temperature Cs-atoms. Such dependence of the flux of

background Cs atoms on the dispenser current has been systematically investigated

in Ref. [84]. Whereas the initial fluorescence counts, which is directly related to

the MOT-density, increases by only ∼1.3 times from I d = 5.2 to 5.6 A. Moreover as

shown in Fig. 4.4(b), the fluorescence signal follows the same decay trajectory, even

when the MOT is switched off. The above observations suggest that the surface is

modified mainly by the background room temperature Cs-atoms and not by the cold

MOT-atoms. This is also reasonable from the theoretical calculations [102], which

show that the phonon-mediated decay rate for room-temperature atoms (∼300 K) is

almost three orders of magnitude higher than that for the cold-atoms (∼100 µK), as

shown in Figs. 4.9(a) and (b). So, the room-temperature atoms may quickly fall into

the surface-potential and may get chemisorbed onto the surface, thereby modifying


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 118

the surface conditions.

In order to explain the enhanced loading of MOTatoms into the surface potential

under the modified surface conditions, we speculate the following mechanism.

The background Cs-atoms which are adsorbed onto the nanofiber surface may form

isolated island like structures and can locally enhance the low-energy phonon mode

density which can facilitate the loading process of MOT-atoms into the surface potential.

Actually, such an enhancement of the low energy phonon-mode density is

theoretically calculated for nanoparticles (∼10 nm) on a substrate [103]. Figure

4.9(c) shows the calculations for phonon-density-of-states with respect to energy for

a silicon structure of diameter 10 nm attached to a silica substrate. There can be

seen many resonance peaks. The high density-of-states at low energy (∼ 30 GHz)

compared to a bulk medium is because of the silica nanparticle induced enhancement

of phonon-mode-density. The phonon-mode density is locally enhanced around the

nanoparticle. But the local low-energy (∼ 30 GHz) phonon-mode-density enhancement

cannot explain the loading process for a depth of energy ∼-100 MHz, which we

observe in the present experiments. We speculate that the loading of atoms in the potential

range of -100 MHz is due to two-phonon enhanced (Raman) scattering process.

Figure 4.9(d) shows the calculated free-to-bound transition rates with respect to the

energy of the surface potential [102]. The calculations have been done for Cs-atom at

200 µK and the phonon bath at 300 K. The top arrow shows the decay into some deep

surface potential from free-state, due to phonon emission and the bottom arrow shows

an upward transition from that lower bound state to an upper bound state (∼ 120

MHz) due to phonon absorption. The loading into the shallow-surface-potential may

be due to this two-phonon (Raman-type) scattering processes. The loading of atoms

in the shallow-surface-potential, due to local enhancements of phonon-mode-density,

can explain the broad spectrum due to bound-atoms in the surface potential.

In the next section, we discuss the mechanism for the observation of free-atoms

Lorentzian and Mollow-triplet lineshape in the excitation and emission spectra respectively,

after irradiating the MOT atoms with an UV laser.


4.4. LIF Spectrum Measurements: Analysis and Discussions 119

(a)

Ionization

Level Cs +

-e

(b)

3.893 eV

407 nm ~ 3.05 eV

Cs-atom islands

Nanofiber

Surface

SiO2

1.33 eV

van der Waal

Potential

Excited State

850 nm ~ 1.46 eV

Free Cs Atom

Nanofiber

(300 K)

-e

Cs

-e

0.66 eV

Ground State

-e

Electron / Ion Bombardment

Energy Levels of Cs-Atom Near Silica Surface

Figure 4.10: (a) The energy level diagram for a Cs-atom near a silica surface showing

the surface potentials and the ionization level. (b) Schematic diagram of the bombardment

of Cs-atom islands adsorbed on to the nanofiber surface by Cs-ions and

photoelectrons.

4.4.3 Effects of UV Laser Irradiation of MOT-Atoms

It has been mentioned in Sec. 4.3.1 that the excitation spectrum shape with a large

red-tail returns back to its free-atom Lorentzian if we again irradiate the MOTatoms

with UV laser. The evolution of the spectrum D to A (Fig. 4.2), with the

irradiation of UV laser suggests that the atomic-islands formed on the nanofiber

surface, which enhances the local phonon-mode-density and assists in loading the

atoms in the surface potential may be cleared away by some process like desorption.

Desorption of alkali atoms from material surface stimulated by the irradiation of

high energy photons ( ∼ 3 eV), is a commonly used technique in atomic physics and is

well known as the light induced atom desorption (LIAD) process [54, 56, 58, 59]. But,

it has been reported earlier [41, 42], and also confirmed in the present experiments,

that the effect of UV laser (407 nm) irradiation occurs only in the presence of MOTatoms.

That is the spectrum shape changes only when MOT-atoms are present during

the irradiation of UV laser. So the observed effect is not due to the conventional LIAD


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 120

process.

The observations shown in Fig. 4.3 can be explained by considering photoionization

of Cs-atoms. Figure 4.8(a) shows the schematic diagram for the energy levels of

a Cs-atom near the silica-surface. The atoms around the nanofiber may be free or

bound to the surface potential. The atoms bound in the shallow-vdW potential are

called physisorbed atoms and they may escape to a free-state or may fall deeper into

the surface potential and finally get bound to the surface defect-sites. The atoms

falling into the surface defect sites are called the chemisorbed atoms. The LIAD process

is the release of these chemisorbed atoms and hence requires photon energy of

3eV(λ ∼ 407 nm). But as already mentioned the present effect is not due to the

LIAD process. As shown in Fig. 4.10(a), the atoms in the MOT after getting excited

by the 852 nm MOT trap lasers can be photoionized in the presence of UV (407 nm)

laser. The MOT atoms can be photoionized following a two-step resonant ionization

process. Such photoionization process has been experimentally investigated in Ref.

[104]. The decrease of fluorescence with UV laser intensity (level S1) as shown in

Fig. 4.3(b), may be understood from the photoionization of MOT atoms, which results

in a loss of atoms in the observation region and hence the fluorescence count

decreases. Also, with time more and more atoms will be ionized in the observation

region and fluorescence counts will decrease with time. Figure 4.10(a) shows that the

ionization of Cs-atoms gives rise to Cs-ions and photoelectrons. We speculate that

such photoelectrons photoelectrons can desorb Cs-atoms or islands from the nanofiber

surface due to electronic excitation in the bulk silica, as has been explained for the

case of sodium desorption from silica surface [56]. Also, the generated Cs-ions may

desorb the atoms or islands from the surface by the process of sputtering. Figure

4.10(b) shows these two processes schematically. The desorption of atomic islands or

the nanostructures, will nullify the local enhancements in the phonon-mode-density

as mentioned before and can prevent the atoms from falling into the surface potential.

The indirect desorption of atoms by UV laser can then explain the free-atoms

spectrum observed just after irradiating the MOT-atoms with UV laser.


4.5. Discussion 121

4.5 Discussion

The excitation spectra shown in Figs. 4.2(A-D), are quite different from the usual

atomic Lorentzian lineshape and shows a large tail in the red-detuned side. Such

difference may be attributed to atom-surface vdW interactions since we are observing

atoms closer than λ/2π from the nanofiber surface. The condition of spectrum D has

been reported in Ref. [40] and is understood from a process where atoms approaching

the nanofiber surface fall into the vdW potential, forming long-range atom-surface

bound states [40, 60, 61]. As discussed in Sec. 4.4.1, the narrow spectrum near

the resonance is due to the contribution from free-atoms making transition from

the free-ground states to the bound-excited states. And the broad spectrum in the

red-detuned side is due to the bound-atoms making transitions from bound-ground

states to the bound-excited states. The adsorption of atoms into such bound-states

may be understood as physisorption process as the depth of such observed interaction

is several orders of magnitude lower than that of chemisorbed atoms (∼ 1 to 3 eV).

The present observations of varying spectral shape with time can be explained from

population distribution of free- and bound-atoms depending on the loading rate into

the surface potential [40]. Especially in the condition of spectrum A the loading

rate is negligible and atoms around the nanofiber behave as free-atoms [42]. The

observations suggest that the loading rate increases with time and as a result the redtail

increases for spectrum B, C and D due to the contribution from bound-atoms.

Moreover the observed emission spectrum shown in Fig. 4.7 shows clear evidence

of bound atoms. The emission spectrum for ∆= +20 MHz excitation shows the

free-atom three-peak spectrum (Mollow-triplet spectrum), whereas spectrum for the

∆= -20 MHz excitation shows a wide bandwidth spectrum with no clear peak like

structure. The observations suggest that by changing the excitation laser frequency,

we are exciting different class of atoms. For ∆= -20 MHz excitation, we are exciting

bound-atoms whereas for ∆= +20 MHz excitation, we are exciting free-atoms. Since

the excited-state surface-potential is twice deeper than the ground-state potential,

there is a surface induced red-shift of the resonance frequency of bound-atoms [60].


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 122

So, for ∆= +20 MHz excitation, bound-atoms will be out of resonance and no atoms

other than the free-atoms can be excited. we note here that for ∆= +20 MHz excitation,

the Rabi-frequency (Ω) calculated from the experimentally measured excitation

beam intensity is found to be larger than that obtained from the theoretical fitting,

and differs by a factor of around 1.9. This difference might be due to the position distribution

of MOT atoms with respect to the intensity profile of the excitation beam,

along the axis of the nanofiber. Also, due to some residual magnetic field in the

MOT region, the dipole moment orientation of the atoms will have some distribution

which may contribute to such deviations in the observed Rabi-frequency. Regarding

the sharp peak due to the elastic scattering, it is understood as scattering from silica

nanofiber, since it is observed without atoms. Elastic Rayleigh scatterings from atoms

may be included in the sharp peak, but the contribution from the Cs atoms should

be much smaller than the bulk-silica nanofiber scatterings. We should mention here

that the high resolution of 250 kHz is crucial as the spectrum of atoms is distributed

within 60 MHz and cannot be resolved by techniques like that used for spectroscopy

of molecules adsorbed on a nanofiber [49].

The loading of atoms into the surface potential can be explained qualitatively

considering atom-phonon coupling. The thermal vibrations of the surface may modulate

the wavefunctions of the approaching cold atoms. The atoms may lose energy

via phonon emission and fall into the vdW potential. However, calculations suggest

that for the temperature range of 100 µK to 400 µK of the MOT atoms, the phononmediated

loading rate into such shallow bound states is almost negligible [102]. This

is due to the fact that the nanofiber is at room temperature (∼300 K) and the low energy

phonon-mode density is rather small. Then the loading into the surface-potential

might be due to modified surface conditions.

The observations shown in Fig. 4.4 suggest that the hot atoms from the dispenser

play a crucial role in modifying the surface conditions. Also, the observation for

I d = 5.2 A, where the fluorescence signal follows the same decay behavior as it was

before switching off the MOT atoms, suggests that it is not the MOT cold atoms but

the hot background Cs-atoms which is responsible for such signal decay. Moreover,


4.5. Discussion 123

according to the theoretical study of phonon-mediated decay rates, the adsorption

probability for hot atoms is two orders of magnitude higher than the cold atoms

[102]. We suspect that at an early stage of such hot-atom surface coating process,

there may be isolated island like structures created on the nanofiber surface. Such

nanostructures may locally enhance the low-energy phonon mode density and hence

the loading process. Actually it has been theoretically calculated that nanoparticles

on a bulk substrate can resonantly enhance the local low-energy phonon mode density

[103]. We note here that the dephasing due to phonons on the bound atoms might be

quite high, but since we are observing the fluorescence from bound atoms, the local

surface potential might be modified due to modifed surface conditions. The behavior

of the local surface potential might be the same as the global surface potential, and

we can observe atoms bound in such local potentials.

The effect of UV laser is yet to be fully understood, but the observations in Fig.

4.2 suggest that the effect of UV laser is to clean the nanofiber surface from any

deposition of Cs atoms. However, the ineffectiveness of the UV beam in absence of

MOT atoms (as shown in Fig. 4.3) suggests that it is not the known light induced

atom desorption (LIAD) process [56, 59]. The observation shown in Fig. 4.3 shaws

that, since we are observing the effect of UV laser only in the presence of MOT

atoms, a two-step (407 nm + 852 nm MOT laser) resonant ionization of Cs-atoms

[104] may play a role in modifying the nanofiber surface. The photoionization process

may generate ionized Cs-atoms along with photoelectrons. Such photoelectrons can

desorb Cs atoms from the surface due to electronic excitation in the bulk silica.

Also, the generated Cs-ions may desorb the atoms from the surface by the process

of sputtering. As a result a clean and ideal surface is realized where the phonon

mediated decay rates are not sufficient to load the atoms into the surface bound states.

The competition between the above mentioned adsorption and desorption processes

determines the nanofiber surface condition and hence control the loading into the

surface potential. In the present emission spectrum measurements, the UV laser

intensity and the dispenser current have been chosen in such a way so as to balance

the adsorption and desorption rates, such that the surface condition as indicated by


Chapter 4. Probing Atom-Surface Interactions Using Optical Nanofibers 124

the excitation spectrum lineshape is kept stable for a long time. Such stable surface

condition is important for investigation of long range atom-surface bound states or

quantum adsorption of atoms [20, 21]. Further experiments are needed to clarify the

surface mechanisms in more details.

One possible way to investigate phonon-mediated loading of atoms in the surface

potential is to deliberately deposit gold- or silver-nanocrystals on the nanofiber surface,

keeping the dispenser current at I d = 4.8 A or less, when the flux of backgroundatoms

and hence number of adsorbed atoms on the surface are less and observing the

red-tail or wide-bandwidth spectrum in the excitation or emission spectrum respectively.

This can provide some concrete evidence that the loading is indeed due to

locally enhanced phonon-mode-density, induced by the adsorbed Cs-nanostructures.

The nanofiber system can be extended to study in details the adsorption and

desorption of Cs-atoms for various surface conditions. As we can directly observe the

fluorescence of near-surface atoms, nanofiber method may open up a new tool for

probing atom-surface interactions.

4.6 Conclusions

We have shown that optical nanofiber can be used as a tool to probe atom-surface

interactions. We have measured the fluorescence excitation spectrum of cold atoms in

the vicinity of the nanofiber. The observed spectrum of such near-surface atoms differs

drastically from the free-space atom behavior, and shows signature of atomsurface

bound-states. We have shown how the excitation spectrum lineshape evolves with

time, due to changing surface conditions. We have experimentally demonstrated

that the spectrum lineshape and hence the loading into such surface bound-states

can be controlled by maintaining the surface conditions. The measured emission

spectra, under such controlled surface conditions, further clarify the behavior of freeand

bound-atoms. We discuss the possible roles of adsorption of background roomtemperature

Cs-atoms and indirect desorption by UV laser irradiation, in controlling

the surface conditions. The present nanofiber system can be extended to investigate


4.6. Conclusions 125

in details the adsorption and desorption of atoms. Moreover, the nanofiber method

can be used to investigate long-range atom-surface bound states. As we can directly

observe the fluorescence of near-surface atoms, nanofiber method may open up a new

tool for probing atom-surface interactions.


chapter 5

CONCLUSIONS AND FUTURE EXTENSIONS OF THE

PRESENT WORK

In this chapter we discuss the conclusions and the possible extensions of the present

nanofiber method for the fluorescence spectrum measurement of atoms.

5.1 Conclusions

We have shown that LIF excitation and emission spectrum of a small number of

strongly-driven cold atoms can be investigated using optical nanofibers. This is because

atoms which lie in the vicinity of the optical nanofiber can emit a significant

fraction of fluorescence photons in the single guided-modes of the nanofiber (∼2 %).

Now, the atoms emitting fluorescence in the guided-modes of the nanofiber lie very

close to the nanofiber surface and are subjected to atom-surface interactions. It has

been reported in earlier experiments on nanofiber, that such surface-interactions can

be modified by irradiating the MOT-atoms with UV laser. After such irradiations,

MOT-atoms are kept from falling into the surface-potential and behave almost like

free-atoms around the nanofiber. We first performed our fluorescence spectra mea-

128


5.1. Conclusions 129

surements under this free-atom conditions. For the emission spectrum measurements,

the optical nanofiber method is combined with OHD technique and PCR spectroscopy.

The combined method is used for the first time for fluorescence emission spectrum

measurements. The spectral resolution in the present emission spectrum measurements

is ∼250 kHz and is limited by the measured correlation time and hence the

dwell-time of atoms around the nanofiber. The emission spectrum measurements

were done by integrating the fluorescence photons for a time of 3 minutes, which is

much less than the time required for free-space measurements. The observed excitation

spectrum lineshape shows almost a free-atom like Lorentzian behavior, with

a very small red-tail. The red-tail has been attributed to photoassociation process,

due to atoms making transition from free-ground states to bound excited states in

the surface induced potential. Under this condition, the observation of Mollow-triplet

emission spectra for both on- and off-resonant excitations confirms the realization of

free-space two-level atoms near the nanofiber surface. The realization of free atoms

can be used for various quantum optical experiments, for example to generate single

photons from single atoms. Also, the quantitative agreement between the observed

emission spectra with the theoretically calculated emission spectra for free-atoms confirms

the optical nanofiber method for measuring LIF emission spectra of atoms. The

present method of LIF measurements using nanofiber, in addition to the combined

OHD and PCR technique, may give a new tool for investigating LIF emission spectra

of strongly-driven atoms.

As mentioned above, since we are observing near-surface atoms, fluorescence measurements

based on optical nanofibers may become a unique tool to probe atomsurface

interactions. In earlier experiments using nanofiber, signatures of atomsurface

interaction have been observed in the excitation spectrum of atoms. The

observed spectrum of such near-surface atoms differs drastically from the free-space

atom behavior, which has been attributed to atom-surface interactions. The lineshape

of the excitation spectrum is understood as a result of the process where atoms approaching

the nanofiber surface fall into the shallow surface potential, forming longrange

atom-surface bound states. It has been found that the excitation spectrum


Chapter 5. Conclusions and Future Extensions of the Present Work 130

lineshape changes with time. Also it has been reported that such surface interactions

can be modified by controlling the flux of background Cs-atoms in addition to the

intensity of UV laser irradiation. In this thesis, we have systematically investigated

such changes in the lineshape of the excitation spectrum and have shown how the

LIF excitation spectrum lineshape evolves with time. The change in lineshape of

the spectrum has been attributed to the changing nanofiber surface conditions. The

experimental observations have shown that hot background atoms play a crucial role

in changing the nanofiber surface condition. Such hot atoms may get adsorbed onto

the nanofiber surface. The theoretical calculations have also shown that hot background

Cs-atoms, have high probability than cold MOT-atoms to get adsorbed on to

a silica-surface. The adsorbed hot atoms can enhance the local phonon-mode-density,

and can facilitate the loading of MOT-atoms in the shallow surface potential. The

MOT-atoms in such shallow surface states show molecular behavior. The UV laser

irradiation of MOT-atoms overlapped with the nanofiber has been found to cause

photoionization of MOT-atoms by a two-step resonant ionization process, and we

speculate that the generated photoelectrons may indirectly desorb the chemisorbed

atoms from the nanofiber surface. We have found that a particular state of the lineshape

of the excitation spectrum can be maintained by controlling the flux of the

background atoms and the UV laser intensity. Under this controlled surface condition,

we have observed the fluorescence emission spectrum. We have carried out the

measurements, for both blue- and red-detuned excitations. The observed emission

spectra confirms the behavior of near surface atoms. We discussed qualitatively the

phonon-mode density for nanofiber at room temperature and the phonon-mediated

decay of atoms in the surface-potential. We discussed the roles of adsorption and desorption

of atoms on the surface conditions. The present system can be extended to

investigate in details the adsorption and desorption of atoms. Moreover, the nanofiber

method can be used to investigate long-range atom-surface bound-states.

The present method of fluorescence measurements using optical nanofibers, in

addition to the OHD and PCR technique, may give a new tool for investigating atom

behaviors in various boundary conditions such as dynamics in the dipole potential. In


5.2. Future Extensions of the Present Work 131

the next section, we discuss the possible extension of the present LIF measurements

using nanofibers to investigate fluorescence of trapped-atoms in an optical-dipole trap

potential, around the nanofiber.

5.2 Future Extensions of the Present Work

Investigation of the fluorescence spectrum of atoms trapped in a dipole potential

can reveal many interesting physics about the atomic motion in the trap potential.

Fluorescence spectrum measurement of atoms in a one-dimensional optical molasses

has has been used to study the localization of atoms by measuring the transitions

between the vibrational levels of the standing wave potential well [23].

As discussed earlier, the propagating field of the guided mode of the nanofiber has

a large decaying evanescent tail, in the transverse direction, just outside the nanofiber

in the evanescent region. The intensity gradient of the field in the evanescent region

can be used to create a dipole potential well for atoms around the nanofiber. The

optical dipole potential depends on the intensity and detuning of the light field. In our

nanofiber case, the steep variation of the intensity of the field in the evanescent region

leads to a gradient force on the atom in the transverse plane. For detuning ∆ large

compared to Rabi frequency Ω and the atomic linewidth γ, the optical potential for

the gradient force can be written as U = Ω 2 /∆. So for a red detuned light (∆ < 0),

the optical potential becomes attractive and for a blue detuned light (∆ > 0) the

optical potential becomes repulsive. The trapping potential can then be created by

the balance between this two optical potentials. The study of a two-color dipole trap

around an optical nanofiber has been carried out by our group [34]. The crucial point

is that the two far off-resonance lights, red- and blue-detuned with respect to the Cs

D 2 -transition, launched into the nanofiber will have substantially different evanescent

decay lengths and can produce a net potential minimum around the nanofiber. The

more the detuning, the more is the trap life time. Due to the conservative character

of optical potentials, the loading of atoms into dipole traps requires the use of friction

forces, which can be provided by the Doppler cooling mechanism for example in a


Chapter 5. Conclusions and Future Extensions of the Present Work 132

(a)

780 nm

910 nm

Atom

F

blue

F red

Nanofiber

Two-Color

Light Waves

(b)

Figure 5.1: (a) Schematic diagram of atom trapping around a nanofiber using a twocolor

trap. The evanescent tail length for the red- and blue-detuned light are ∼450 nm

and ∼250 nm respectively. The force due to red-detuned light is attractive whereas

force due to blue detuned light is repulsive. (b) Two-color trap potential calculated

as a function of distance of atom from the nanofiber surface. The Cs D 2 transition

corresponding to a wavelength of 852 nm has been considered for the calculations.

The fiber radius is a = 200 nm. The wavelengths of the red- and blue-detuned light

and their powers used for the calculations are also shown in the plot. A trap depth

of -1.24 mK, and a trap life time of 35 s has been estimated with the mentioned

detuning and the power parameters.


5.2. Future Extensions of the Present Work 133

MOT [79, 106]. So for loading these traps, the atoms must be precooled in a MOT

and the trap is loaded by overlapping with MOT. Recently, such a two-color trap,

with a trap lifetime of 50 ms, has been demonstrated using a nanofiber [46]. With

such a long lifetime, the resolution of the present spectrum measurement (300 kHz,

corresponding to a lifetime of 2 µs for MOT atoms) can be improved by almost three

orders of magnitude.

Figure 5.1(a) shows the schematic diagram of atom trapping around a nanofiber

using a two-color trap. Figure 5.2(b) shows the net trap potential created by the

two-color trap around the nanofiber as calculated in Ref. [34]. the colors used are

910 nm for the red detuned light and 780 nm for the blue detuned light. A trap

depth below ∼-1 mK can be reached using such a trap and the trap location from

the nanofiber surface is also within the flurescence coupling region of the nanofiber.

We have developed the trapping lasers for both the 910 nm red-detuned laser and

the 780 nm blue-detuned laser. Both are ECDL based home built lasers. For 780

nm laser, which requires high power for trapping, we have used a tapered amplifier

system to amplify the power of the master 780 nm ECDL laser. Also, since high

power is applied through the nanofiber, sharp cut-off filters are used to suppress

the background photo-luminescence of the fiber itself. The fiber scattering is a very

serious issue and may completely dominate the fluorescence signal of the trapped

atoms. The experiments are performed by switching the trap lasers off for a small

duration (less than the trap oscillation time) and measuring the atomic fluorescence

during this off time. The timing circuit, based on the NI-digital waveform generator

as discussed in Chap. 2, has been used to generate the fast timing pulses for driving

the AOM’s in the experiments. The trapping experiments are now in progress in our

laboratory.


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appendix A

EXPRESSIONS FOR THE CORRELATION FUNCTIONS

The detailed theroetical analysis for photon correlations in multiatom fluorescence

emitted into the guided mode of a nanofiber can be found in Ref. [43]. We discuss

here briefly the assumptions and the theory in more detail. We examine fluorescence

from a gas of N identical two-level atoms into guided modes of a nanofiber. The

atoms are pumped by a plane-wave pump field propagating perpendicularly to the

fiber in a travelling wave configuration. We assume that the transition frequency of

the atoms is well below the cutoff frequency of the fiber, so the single-mode condition

[31] is satisfied. In view of the very low losses of silica in the wavelength range of

interest, we neglect material absorption. We also neglect the interaction and collisions

between the atoms.

Let the atoms be at points (r j ,ϕ j ,z j ), where the index j =1, 2,...,N labels the

atoms and the set (r, ϕ, z) is the cylindrical coordinates with z being the axis of the

fiber. We assume that the atoms have the same transition frequency ω 0 and that the

electric dipole vectors d j of the atoms have the same magnitude d = |d j |. However,

the atomic position and the dipole orientation are random in space. The quantum

light field can be decomposed into the contributions from guided and radiation modes.

150


151

We assume that the number of atoms in the atomic cloud is a random quantity and

satisfies the Poisson statistics, with the average number n.

At the exit end of the fiber, the guided field excites free-space modes. The transverse

positive-frequency component of the electric part of the output field is given

by

E(z,t) =


2ω0

cɛ 0

A(z end ,t− (z − z end )/c). (A.1)

where A(z,t) =(2π) ∫ −1/2 ∞

dω a

0 ω (t)e −i(ωt−βz) is the Fourier transform of the photon

operator a ω , with β being the longitudinal propagation constant. Here z ≥ z end , with

z end being the coordinate of the exit end of the fiber.

We study the correlations between the fields measured at two time points (t) and

(t + τ). We consider the far zone where the distances from the observation points to

the atoms are much larger than the light wavelength λ 0 =2πc/ω 0 . In this zone, we

can ignore the field in the radiation modes and hence focus on the field in the guided

modes. By definition, the first and second-order correlation functions of the emitted

photons are given by 〈E ⋆ (t)E(t + τ)〉 and 〈E ⋆ (t)E ⋆ (t + τ)E(t + τ)E(t)〉 respectively.

Here τ is the delay time. The second order correlation function 〈E ⋆ (t)E ⋆ (t + τ)E(t +

τ)E(t)〉 or 〈I(t)I(t + τ)〉 from the Eq. 43 of Ref. [43] is given by

〈I(t)I(t + τ)〉 = Z 2 [NDΓ (2) (τ)+N(N − 1){M 2 o ρ 2 ee + M 2 | Γ (1) (τ) | 2 }]

(A.2)

where ρ ee = 〈σ † σ〉 =Ω 2 /(2Ω 2 +Γ 2 ) is the population of the excited atomic state.

where Ω is the Rabi frequency of the excitation beam and Γ is the modified linewidth

of the atom due to presence of the nanofiber. Here the pseudospin operators σ and

σ † describe the downward and upward transitions of the atoms, respectively. The

correlation function can be further simplified as

〈I(t)I(t + τ)〉 = I2

n 2 µ 0

{

ng (2) (τ)+n 2[ µ 0 + µ|g (1) (τ)| 2]}

(A.3)


Appendix A. Expressions for the Correlation Functions 152

where g (1) (τ) =Γ (1) (τ)/ρ ee and g (2) (τ) =Γ (2) (τ)/ρ 2 ee are the normalized first- and

second-order correlation functions respectively. The coefficient µ 0 = M0 2 /D and µ =

M 2 /D. The coefficient I = 〈E ⋆ (t)E(t)〉 is the intensity of the fluorescence light. The

expressions for single atom correlation functions can be found in the Appendix of Ref.

[43] and are given by

Γ (1) (τ) =〈σ † (t)σ(t + τ)〉

Ω 2 [

Γ 2

=

2Ω 2 +Γ 2 2Ω 2 +Γ + 1 2 2

e−

Γτ

2

+ 1 ]

3Γτ

e− 4 {P Cosκτ + QSinκτ}

2

(A.4)

Γ (2) (τ) =〈σ † (t)σ † (t + τ)σ(t + τ)σ(t)〉

Ω 4 [

=

1 − e − 3Γ

]

3Γτ

(2Ω 2 +Γ 2 ) 2 4 {Cosκτ +

4κ Sinκτ}

(A.5)

The expression for coefficients P, Q and κ are given by

P = 2Ω2 − Γ 2

2Ω 2 +Γ 2 ,

Q = Γ 10Ω 2 − Γ 2

4κ 2Ω 2 +Γ , 2


κ = Ω 2 − Γ2

16

The expressions for the coeffcients M 0 ,M, and D are given as

M 0 = 1 3 〈|e r| 2 + |e ϕ | 2 + |e z | 2 〉 r ,

M = M 0 δ lal b

+ 1 6 〈(|e r| + |e ϕ |) 2 +〉 r δ lal −b

,

D = 1 5 〈|e r| 4 + |e ϕ | 4 + |e z | 4 〉 r + 2 15 〈|e r| 2 |e ϕ | 2 + |e ϕ | 2 |e z | 2 + |e z | 2 |e r | 2 〉 r

+ 4

15 〈|e ϕ| 2 |e z | 2 〉 r .

Here the notation 〈···〉 r =[(rmax 2 − a 2 )/2] ∫ −1 r max

···rdr stands for the statistical

a

averaging over the radial distance r. e r ,e ϕ and e z are the mode profile functions

for the guided modes, and l a and l b denote the polarization of the guided modes.


153

The expression for the proportionality factor Z is Z =(ω 0 d 2 /ɛ 0 v g )=(3λ 2 0 n gΓ 0 /8π).

Here Γ 0 is the natural linewidth of the atoms, and n g = c/v g is the group index of

the fiber.


appendix B

OPTICAL-HETERODYNE TECHNIQUE MEASUREMENTS

Figure B.1 shows the schematic of the experimental setup used for OHD-technique test

purposes. The test has been done with and without the lock-in-amplifier (LIA) based

detection. The figure shows two lasers phase-locked with each other. The beat-signal

between the two lasers is 45 MHz, including the AOM-frequency shifts. The beat

signal is observed on an APD detector (Hamamatsu, APD, C47777). The detector

output is then analyzed on a spectrum analyzer. Figure B.2 plots the detected beatsignal,

for different LO-powers, keeping the signal-power fixed, and without the LIAdetection.

The test has been performed with high signal-power (∼1 nW) to check

the LO-power for shot-noise limited detection. As can be seen from the figure, with

increase in LO-power the background-noise is increasing, implying that the LO shotnoise

is dominating the detector noises (Johnson noise, dark current noise etc.). The

signal-to-noise ratio (S/N) is increasing, confirming the fact that we are still in the

shot-noise limited detection window, and have not reached the point where amplitude

fluctuations of the LO-laser start dominating, because in that case the S/N would

have started decreasing. But from 530 nW to 1 µW, the background and S/N level are

same, showing that the detector is working near its saturation point, mainly because

154


155

ECDL

(LO)

-45MHz

PLL@80MHz

ECDL

(Signal)

+125MHz

AOM

APD

Spectrum

Analyzer

ND filter

10Hz

SYNC

Lock-in

Amplifier

PC

Figure B.1: Experimental set-up for the beat measurement between two lasers with

phase sensitive detection

Figure B.2: The beat signal between the two lasers for a fixed signal power and

different LO powers. The spectrum analyzer settings are also shown in the figure.


Appendix B. Optical-Heterodyne Technique Measurements 156

(a)

(b)

Figure B.3: (a) Measured beat signal between lasers for fixed local oscillator power of

0.8 µW. The LIA phase sensitive detection has not been used. The spectrum analyzer

settings are also shown in the figure. (b) The sensitivty acheived with phase-sensitive

detection are 0.55 fW/ √ Hz.

of the saturation of the integrated low-noise pre-amplifier of the detector. The datasheet

also validates this point of 0.8 µW saturation power for the detector. Figure

B.3(a) shows the detected beat-signal for a LO power of 0.8 µW. The figure shows

that, a minimum signal-power of 20 pW distributed in a frequency range of 10 kHz

can be detected with a reasonable S/N.

Figure B.3(b) shows the beat signal when the LIA is included in the setup and

the AOM is modulated with a frequency of 20 Hz. The figure shows that upto 55

fW of laser power can be detected with S/N of ∼ 1. The band-pass filter BP30 has

a Q-value of 30 and 3-dB detection bandwidth of ∼ 1.2 Hz.


appendix C

DFB FEEDBACK-CIRCUIT DETAILS

5k

R3

560

X1

R2

510

R1

10n

Monitor Output

DBM Input

10Meg

1K

R4

1K

R5

10k

R6

X2

S1

1u

C1

X3

C2

VR2

10k

50%

3k

R8

3k

R9

3k

R10

X4

3k

R11

For LD feedback

R7

VR1

10k

50%

Figure C.1: Feedback circuit used for the DFB cooling and repump lasers.

OP-AMP’s used are OP-27.

The

158


appendix D

DEVELOPMENT OF A GLASS-CELL MOT SYSTEM

We have developed another MOT-system with the nanofiber in vertical-orientation.

The new MOT-system consists of a pyrex-made glass-cell and will allow us to do

experiments with more flexibility. The added advantages are:

• For experiments requiring better optical-access.

• Fast-switching of magnetic-fields : Absence of any Eddy-currents due to glass

structure.

• Fast generation of MOT-atoms with extra-lifetime : By the process of light

induced desorption, generation of atoms only when necessary and reducing the

background-atom density and collisions.

Figure D.1 shows the schematic diagram of the glass-cell MOT system. The glasscell

sits on top of one of the ports of a six-way cross (made of stainless-steel). One of

the other ports is used as an outlet for one-end of the nanofiber. Another end of the

nanofiber comes out from the top of the glass-cell. Two of the ports of the six-way

cross is connected to turbo- and ion-pumps, through gate valves. The fifth port is

160


161

used for the dispenser current and other electrical feedthroughs. The sixth-bottomport

consists of a glass window, for optical access. The holder of the nanofiber

is specially designed, so that it can be introduced into the glass-cell, as shown in

the photograph (Fig. D.1). For added flexbility, we have connected a high-vacuum

compatible temperature sensor and a heater to the holder structure, to straighten

up the nanofiber, for nanofiber-cavity based experiments. The total system is baked

up, to achieve high-vacuum, and care has been taken that all the components inside

the chamber are clean and are compatible with high-vacuum conditions. We have

reached a vacuum of 10 −9 mbar in this setup. Figure D.2(a) shows the photograph of

the MOT-system. There can be seen two optical breadboards, one on top of another.

The glass-cell can be seen in between the two magnetic-field generating coils, on the

bottom breadboard. The coils are fixed on a 3-axis translational stage which resides

on the topmost breadboard, and are hanging. Their position can be finely tuned with

the help of the micrometer-screws of the stage. A support has been provided between

the coils, just above the glass-cell, to stop independent movements and to avoid any

oscillations. Two of the MOT-trapping beams are shown in Fig. D.1, with the third

beam perpendicular to both the beams. We use a three-way beam for creating the

MOT. The optics for the MOT is placed either on the optical breadboard or fixed onto

the supporting pillars and posts, shown in Fig. D.2(a). We use the same trapping

lasers, as mentioned in Chapter 2, for creating the MOT. Figure D.2(b) shows the

CCD-camera view of the MOT-cloud for a dispenser current of 5 A. The scattering

of MOT-trapping lasers due to the glass-cell wall can be seen. With this system, we

are able to generate Cs-MOT by light-induced-desorption of atoms due to violet-LED

irradiation of the pyrex-glass cell. Moreover, single-atom detection using nanofibers

has been demonstrated using this setup and experiments based on fast-switching of

magnetic-field has been investigated.

We hope that the glass-cell MOT setup combined with optical nanofibers, can

become a valuable tool for experiments in the future.


Appendix D. Development of a Glass-Cell MOT System 162

Nanofiber-End

4

54

100

MOT-Beams

48

Glass-

Cell

100

150

8

Optical Bread-Board

12.7

To

Turbo-

Pump

Nanofiber-End

173

Angle-Valve

70

105

62.5

6-Way Cross

10

35

Optical Table

Figure D.1: The schematic diagram of the glass-cell MOT system. The drawing is

not to the scale. The dimensions are shown in mm.The photograph of the glass-cell,

with the nanofiber holder inside the cell. The nanofiber is fixed in the same way as

described in Chapter 2. The MOT coils can be seen on both-sides of the cell.


163

(a)

(b)

CCD-View

Figure D.2: (a) The photograph of the glass-cell MOT system. (b) The CCD-camera

view of the MOT-cloud fluorescence in the cell.


Acknowledgements

I would like to thank Prof. Kohzo Hakuta for his guidance and constant encouragement

throughout this work. I am grateful to him for giving me the opportunity to

work in his laboratory and to gain so much knowledge and wisdom. Prof. Hakuta

trained me to think logically based on scientific facts and to make conclusive decisions.

Decisions which vary from, which instruments to buy to which direction to proceed

in case I got stuck with some research problem. He taught me how to present and

write some experimental work scientifically. We were always welcome in his room to

discuss physics, without any prior appointments, inspite of his busy schedule. Still

I have lots of thing to learn from him and I hope that my thirst for learning never

ends.

I would like to thank my laboratory seniors and colleagues who helped me, not

only in the experiments but also in my daily life during my stay in Japan. I would

like to thank my friend Dr. Kali. P. Nayak who helped me during my entire stay

in Japan and I am fortunate enough that his stay in our laboratory overlapped with

mine. Kali is the first person who, while pursuing his ph.D. under Prof. Hakuta,

demonstrated the work on fluorescence excitation spectrum measurement and its

use in studying atom-surface interaction, using optical nanofibers and hence for the

present work his collaboration was very crucial. The nanofiber fabrication work in

our laboratory itself started a few years earlier than Kali’s work, and I would like to

thank Dr. Liang San, and the graduate students who worked on the fabrication of

the nanofiber. I would like to thank Tomonaga San, who was a master student under

Prof. Hakuta, who started the work on fluorescence emission spectrum mesurement

of atoms using optical heterodyne technique. Later another two students, Shirasaki

San and Miyazaki San took this work further, and it is from their work that my main

work on fluorescence spectrum measurement actually begins. I would like to thank

especially Shirasaki San, for helping me during the fluorescence emission spectrum

measurements. I owe him a lot, not everything but a lot. I would also like to thank

the present members of our laboratory.


I am very grateful to Prof. Fam Le Kien, who helped me to understand the

theoretical part of our nanofiber experiments and here also I am very fortunate to

have access to him through out my ph.D. studies. He helped me to develop the theory

for the combined method of optical hetrodyne technique with photon correlation

spectroscopy. I would like to thank Morinaga Sensei of Institute of Laser Science

in our University to teach me various experimental details. I would like to thank

Prof. Katsuragawa for giving valuable insights for my work. I am also grateful to

Prof. Nakagawa, to explain me the magnetic field switching system for magnetooptical

trap and also lending us the high vacuum sealant for our atom trap system. I

would like to thank Prof. Suzuki for teaching me on many occasions, how to use the

drilling and milling machines for making some custom structures. Here I would like

to come back again to Prof. Hakuta, who taught me some fundamental things about

making custom structures made of aluminium and stainless steel. Prior to coming to

this laboratory, I did not have any idea on machining, and I have no hesitation in

disclosing that I did not know even the fact that two structures when combined or

joined by screws, one structure atleast should have through holes for the screws. I

would also like to thank Okuno Sensei for showing me how to calibrate a scanning

electron microscope.

I would like to thank the members of review committee for my ph.D. work. I

would like to thank Prof. Hakuta, Prof. Ken-ichi Nakagawa, Prof. Chikashi Yamada,

Prof. Shinichi Watanabe, Ass. Prof. Tsuyoshi Okuno, and Ass. Prof. Norihito

Sogoshi for their suggestions and comments to improve my thesis further.

I would like to take this opportunity to thank Ishii San, who used to handle the

official works in our laboratory. Without her help, it would have been very difficult

for me to live a smooth life in Japan. I am deeply indebted to her and would always

remember her as a person who never gives a second thought on helping others. I

would also like to thank Yamazaki San, who is presently in charge of the official

works.

I would like to thank Dr. Suzuki San and Dr. Fuji San, who were working as

post docs in Katsuragawa laboratory during my phD period, for helping me in my


esearch. I am indebted to my Japanese language teachers Tanaka Sensei, Miyoshi

Sensei and Ooki Sensei who taught me the basic Japanese languages and introduce me

to the Japanese culture. I am also grateful to my other Japanese language teachers

Shimada Sensei and Oohori Sensei, who taught me Japanese language in a local

volunteer society.

My special thanks to my teacher Prof. S. Dutta Gupta, who taught me electromagnetism

during my master studies at University of Hyderabad, India and who was

very kind to introduce me to Prof. Hakuta and his works. Without him, I would

never have the opportunity to visit this laboratory and perhaps would have pursued

another career. I will be always grateful to Prof. Dutta Gupta.

I would also like to acknowledge my friends here, both inside and outside the

University campus, especially Gopi, Raju, Manasa, Ram, and Srinu.

Finally, this thesis would not have been possible without the support of my Father,

Mother and my Sister. My father pushed me hard to go for my master studies

at University of Hyderabad and during that time kept reminding me to pursue higher

studies instead of giving in to some job. My Mother supported me during my entire

phD studies. And I would like to mention my Sister here, who actually was instrumental

in making this phD study a reality, by taking care of my home and my Mother

during my absence from home. I would like to dedicate my thesis to my Parents and

my Sister.


Author Biography

Manoj Das was born in Kolkata, India, on May 13, 1981. He recieved the B.Sc degree

in Physics from University of Calcutta, Kolkata, India, in 2002, and the M.Sc (Tech.)

degree in Electronics from University of Hyderabad, Hyderabad, India in 2005. He has

been with the Department of Applied Physics and Chemistry, University of Electro-

Communications, Tokyo, Japan, working towards the Ph.D. degree. His research

interests include the use of ultrathin optical fibers or optical nanofibers in the study

of laser induced fluorescence spectrum of a small number of atoms, and to investigate

atom surface interactions. Mr. Das is a member of the Japanese Physical Society.

List of Publications Related to the Thesis

1. Manoj Das, A. Shirasaki, K. P. Nayak, M. Morinaga, Fam Le Kien, and K.

Hakuta, “Measurement of fluorescence emission spectrum of few strongly driven

atoms using an optical nanofiber,” Opt. Express 18, 17154-17164 (2010).

2. K. P. Nayak, Manoj Das, Fam Le Kien, and K. Hakuta, “Probing atom-surface

interaction using an optical nanofiber,” (Submitted to Phys. Rev. A).

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