Scalable quantum networks with atoms, photons, and “spins ... - KIAS

Scalable quantum networks with atoms, photons, and “spins ... - KIAS

Scalable quantum networks

with atoms, photons, and “spins”

Kyung Soo Choi

Research Scientist

Institute of Quantum Information and Matter, Caltech

IQIM associate

California Institute of Technology

2012 Open KIAS Winter School on Quantum Information Science

Funding sponsors: NSF/North. Grumm./DoD/AFOSR MURI/IQIM/KIST institutional program

Lecture Outline

Lecture #1: Model-independent verification

of non-classicality and entanglement

Lecture #2: Experimental realizations of

quantum memory and quantum interfaces

Lecture #3: Scalable quantum networks

with atoms, photons, and spins

Quantum revolutions

When “quantum” grows larger

Invention of laser

Bell lab (1957)

Non-local order = Quantum entanglement


Bose-Einstein condensation

Boulder, MIT (1995)

e.g., Multipartite entangled spin waves

Choi et al. Caltech (2010)

2 mm

Simon and Vedral: Natural mode entanglement in BEC

Quantum revolutions

Fundamental physics and technology innovation

When, where, how, and what about it

1. Can quantum coherence exist in many-body systems, either

spontaneously acquired or externally induced and be preserved

2. How do we measure, manipulate, and utilize entanglement in

quantum macroscopic systems

(e.g. spin-waves in atomic ensembles)

Spontaneous formation of quantum phases

Superfluidity in liquid He 4

Superconductivity, BCS state of cooper pairs


Mott Insulator


Condensed matter physics &

Atomic physics

Quantum dynamics of

open quantum systems

Stimulated coherence via

quantum control and measurement

Quantum memories

Quantum processors

Quantum interfaces


Quantum information science


omputer & information science,

quantum machanics, and

quantum statistical mechanics

Many-body physics and emergence of nonlocal orders

“More is different” P. Anderson

“A Different Universe” R. Laughlin

Entanglement and quantum critical phenomena

Moore’s law and

“Quantum transistors”

Fundamental Physics & Technology Innovation

Interdisciplinary Research


AMO physics, quantum optics,

nanoscience, surface physics,

and near-field optics …

Quantum information science

Quantum network as a unifying theme

Information theory

information is physical!

channel capacity,

super-dense coding …



Wiesner (1970)



disembodied transport

Information reconciliation & privacy

amplification: Bennett (1992)

Quantum Computation

Computer science Quantum algorithms

Turing (1936)

Deutsch (1992)

Deutsch (1985)

Shor (1994)

Grover (1996)



Shor, Steane (1995)

Preskill (1997)



Optical clocks

Quantum cryptography

non-local & perfectly secure

Bennett & Brassard (1984)

Ekert (1991)



Entanglement in light

harvesting complexes

and avian compass

Quantum Networks



Spin transport over a

quantum network

Entanglement percolation



Feynman (1982)

Lloyd (1995)



Information transfer in

black hole

Gravitational wave detector

Quantum networks

Bridging the formal and the physical

Quantum node

generate, process, store

quantum information locally

(Internal states of atomic Cs)

Distributed quantum computing

Scalable quantum communication

Quantum resource sharing

Quantum simulation

Quantum channel

transport / distribute

quantum entanglement over

the entire network


Quantum interface

map quantum resources into

and out of photonic channels

(strong coupling)

Quantum Internet

Kimble, Nature (2008)

Theoretical issues

• Characterization of multipartite quantum systems:

computationally intractable

• Quantum computation, communication & metrology

Experimental implementation

• Physical processes of atomic ensembles to reliably generate, process

& coherently control quantum states of matter and light

Quantum networks

Platform for quantum many-body physics

Quantum simulation

• Richard Feynman, 1982; Seth Lloyd, 1994

• Bose-Hubbard model (BEC-Mott insulator), quantum magnetism (Ising spin, spin glass),

superconductivity (BCS-BEC crossover), quantum chemistry (ultracold molecules)

• Simulating non-equilibrium dynamics of quenched systems (Eisert, 2008)

Scaling behavior of entanglement in quantum many-body systems

• Scaling of multipartite entanglement in 1-D spin chains (Kitaev, 2005), entanglement

characterization of multipartite systems (e.g., entanglement spectrum) for condensed matter

physics (Haldane, 2008; Amico et al. Rev. Mod. Phys. 2008), entanglement classification

(Horodecki et al. Rev. Mod. Phys. 2009)

Optimizing a quantum network

• “Entanglement” percolation (Acin, Cirac, Lewenstein Nature Phys. 2007.)

Quantum node


Quantum channel

Enable wide ranges of

interactions by connecting


Quantum interface

Catalyze spin-spin interaction,

engineering of an effective

spin-spin Hamiltonian

Atomic internal states

Rudimentary steps towards quantum networks

Lego boxes for quantum networks

• Heralded capabilities for quantum


• Deterministic capabilities for reversible

transfer of entanglement between matter

and light

• Entanglement of spin-waves shared

among four quantum memories

• Towards integrated quantum systems

with cold atoms in a nano-fiber trap

Scalable quantum networks

with atoms, photons, and spins

Part 1 –

QIP with atomic ensembles in free-space


• “Optical Coherence and Quantum Optics” by L. Mandel and E. Wolf

• “Quantum Optics” by M.O. Scully and M.S. Zubairy

• “Atom-Photon Interactions” & “Photons and Atoms”

by C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg

• “Quantum physics in one dimensions” by T. Giamarchi

Review articles:

• B. Lounis and M. Orrit. Single photon sources. Rep. Prog. Phys. 68, 1129 (2005)

• H.J. Kimble, The quantum internet, Nature 453, 1023 (2008)

• A.I. Lvovsky, B.C. Sanders & W. Tittel, Optical quantum memory.

Nature Photon. 3, 706 (2009).

• K. Hammerer, A.S. Sorensen, E.S. Polzik, Quantum interface between light and matter

Rev. Mod. Phys. 82, 1041 (2010)

• N. Sangouard, C. Simon, H. de Riedmatten and N. Gisin,

Quantum repeaters based on atomic ensembles and linear optics,

Rev. Mod. Phys. 83, 33 (2011)

Matter-light quantum interface

What’s inside here

• Ensemble of ~10 6 Cs atoms released from MOT

• Utilize strong interaction

of single-photons and

collective spin excitations (in the single-excitation regime)

• Input-output coupling κ(t) user-controlled externally by lasers

• Duan, Lukin, Cirac & Zoller (Nature 414, 413 (2001))

Non-collinear geometry:

Harris group (2005)

Writing and reading collective spin waves

Read-out processes:

adiabatic - EIT, offresonant


non-adiabatic - echo type


optical depth

Atomic ensembles in CV regime : Hammerer, Sorensen, Polzik Rev. Mod. Phys. 82, 1041 (2010)

Collective interaction between single excitations and photons

Collective atomic modes : single-mode approximation for pencil-shaped ensembles (Raymer, 1985)

Rigorously, group contraction (Arecchi, 1972) and Holstein-Primakoff transformation (Holstein, 1940)

Formation of dark states : dark-state polariton (Fleischhauer and Lukin, 2001)

Creating single spin waves in atomic ensembles

• Generation of two-mode squeezed state between

Raman scattered field 1 and collective spin excitation

• Detection of a single photon creates a single

collective excitation in a heralded fashion

• Collective enhancement manifested in the quantum


Mapping single spin waves to single photons

• Coherent mapping of quantum states from matter to light (field 2)

• Collective enhancement manifested in the retrieval efficiency

phase-matched radiation into a forward mode

Timed Dicke state: single-photon superradiance

Quantum eraser interpretation for single-photon superradiance of N A atoms (Scully & Zubairy, 2003)

• Phase-matching condition preserved by spin-wave quantum memory

• Constructive interference of the transition amplitudes for writing and reading processes leads to directional

radiation of a single excitation

ground state

PRL 96, 010501 (2006)


conditional absorption



symmetric Dicke state 1

PRL 96, 010501 (2006)

FIG. 4 (color online). The writing and

two atoms in a double-Raman scheme






Superradiance for an inverted two-level system (Dicke, 1954)


Collective Lamb shift in single-photon superradiance (Rohlsberger et al. Science 2010)

j P je i ~k p

~k ~r jj 2 ’j P sche

je i ! bc=c ^n ~r jj 2conN

the cross terms (of different atoms) Ci

The Raman emission doublet (RE cess

Fig. 3(c) has the state vector obtaine mos

case in Ref. [11] as




j Ni RED p X G

k ~ g ~qe i ~k p

~k spon d


N 2 ~ of t

j; ~k; ~q ~q ~k ‘‘co



k ~ g a co

3 3

~q 2 para


V 2 ~ mat

~k; ~q


FIG. 4 (color online). The writing and reading processes of



two atoms in a double-Raman scheme is actually j1

k ~ ; 1 a quantum

~qi; H.




where L

k; ~ ~q ~q ! ac 4 i Rob


4 i ~ 1 and ~ p

j P 2 =4

je i ~k 2


~k ~r jj 2 ’j P No.

je i ! bc=c ^n ~r jj 2

Timing N since is everything the sum of all !

the cross terms (of different atoms) of the is Stokes zero. ( ~k) and anti-Stokes ( ~q

superradiant decay

ground state

Overview: Ensemble-based QIP and their variants

Ensembles of cold atoms

• H. J. Kimble, Caltech (2003)

• A. Kuzmich, Georgia Tech

• S. E. Harris, Stanford

• V. Vuletic, MIT

• J.-W. Pan, Heidelberg

• M. Kozuma, Tokyo

• J. Reichel, Paris …

Entangled ensembles via single-photon bus

Vuletic group, MIT (2008)

Ensembles of trapped ions

• D. Wineland, NIST

• R. Blatt, Innsbruck

• V. Vuletic and I. Chuang, MIT

• M. Drewsen, Aarhus









Ion trap







¬3/2 ¬1/2 +1/2 +3/2

¬3/2 ¬1/2 +1/2 +3/2

¬3/2 ¬1/2 +1/2 +3/2

Solid-state ensembles

¬1/2 +1/2

¬1/2 +1/2

¬1/2 +1/2

c • N. Gisin, Geneva

• M. Lukin, Harvard

100 µm

• R. Schoelkopf, Yale


• J. Schmiedmayer, Vienna …






100 µm




Strong coupling of an ion crystal to optical cavity



Optical pumping


¬1/2 +1/2 P 1/2

¬1/2 +1/2


-1/2 +1/2

1/2 P

Drewsen group, Aarhus (2010)


D S1/2 3/2

D 3/2

S1/2 S1/2 D 3/2

Room-temperature atomic ensembles

• M. Lukin, Harvard (2003)

• A. Lvovsky, Calgary

• P. K. Lam, Canberra …

Figure 1 | Schematic diagram and ion Coulomb crystal images. a, Schematic diagram of the experimental set-up with the linear radiofrequency ion trap

incorporating an optical cavity along its radiofrequency-field-free axis (z axis). The incoupling mirror of the cavity is mounted on a piezoelectric transducer

(PZT) allowing for tuning of the cavity around the atomic resonance. LC: laser cooling beam, RP: repumping beam, OP: optical pumping beam, PP: probe

pulse, RB: reference beam, CM: cavity mirrors, PZT: piezoelectric transducer, CCD: CCD camera, APD: avalanche photodiode. b, Energy levels of 40 Ca +

including the relevant transitions for the three main parts of the experimental sequence. First, the ions are Doppler laser cooled by driving the

4s 2 S1/2–4p 2 P1/2 transition using 397 nm laser beams and repumping on the 3d 2 D3/2–4p 2 P1/2 transition by light at 866 nm. Next, the ions are optically

pumped into the mj =+3/2 Zeeman substate of the 3d 2 D3/2 level using the optical pumping beam in combination with the laser cooling beams. Finally, the

coupling of the Coulomb crystals to the cavity field is measured by injecting a weak probe pulse of 866 nm light into the cavity and detecting the reflection

signal by an avalanche photodiode. c,d, Projection images of a 1-mm-long ion Coulomb crystal recorded with the CCD camera by collecting 397 nm

fluorescence light emitted during laser cooling: the whole crystal (c) and ions within the cavity mode volume (d) (see the text for details).

Strong coupling of electron spin

mode of the cavity, a 1.4-µs-

spatial filtering (Fig. 1a).


3d 2 D3/2-level of 40 Ca + (lifetime: ⇥1s) using a beam making an

angle of 45 with respect to the z axis and having a proper elliptical

polarization (Fig. 1a,b).

To investigate the collective coupling of the ions in the

Coulomb crystal to the TEM00

long and 99%-mode-matched probe pulse is injected. The field

strength of this pulse corresponds to an average intra-cavity

injected into the cavity as a reference of the cavity fluctuations

and drifts. Photons in the probe pulse and the reference beam are

detected in reflection and transmission, respectively, by avalanche

photodiodes with an overall efficiency of 16% after spectral and

An accurate way to quantify the strength of the collective

coupling is, for a series of detunings of the probe frequency

Matter-light quantum interface

1. Generate QI 2. Store QI 3. Process QI 4. Transfer QI from matter to light

Cold atomic ensembles

a. Laser cool 10 11 Cs atoms to ~ 100 µK

(localizations of atoms in a Sisyphus cooling)

b. Hyperfine, Zeeman pumping to ground states

c. Store the qubits in the ground state coherence

(9 GHz clock states of Cs)

d. Operate the quantum interface, detect QI

(repeat a-d)

6P 3/2

6S 1/2

Atomic QI

Pseudo atomic spin

Photonic QI

Matter-light quantum interface

4. Detect QI 3. Store QI 2. Process QI 1. Transfer QI from light to matter

Cold atomic ensembles

a. Laser cool 10 11 Cs atoms to ~ 100 µK

(localizations of atoms in a Sisyphus cooling)

b. Hyperfine, Zeeman pumping to ground states

c. Store the qubits in the ground state coherence

(9 GHz clock states of Cs)

d. Operate the quantum interface, detect QI

(repeat a-d)

Atomic QI

Pseudo atomic spin

Photonic QI

Heralded capabilities for quantum communication (since 2006)

Entanglement generation




( 10 01 )


= +

Investigation of the relationship between

global dynamics of entanglement

and the decay of local quantum correlations

Phys. Rev. Lett. 99, 180504 (2007)

3 m


• Entanglement generated by quantum

interference in the measurement process

• Heralded entanglement stored in the collective

excitations of atomic ensembles

• Degree of entanglement stored in the

ensemble 1

• C = 0.9 +/- 0.3

• Asynchronous preparation – sub-exponential scaling 2

• Functionality achieved by parallel operations

• Quantum cryptography and teleportation

Conditional control of heralded entanglement

Science 316, 1316 (2007); New J. Phys. 9, 207 (2007)

Entanglement connection

Initial work: Chou et al. Nature 438, 828 (2005).


Laurat, Choi et al. Phys. Rev. Lett. 99, 180504 (2007).


Chou et al. Science 316, 1316 (2007); Laurat et al. New J. Phys. 9, 207 (2007)




Deterministic capabilities for quantum-state transfer

Coherent and reversible mapping via dynamic EIT

Photonic entanglement Atomic entanglement Photonic entanglement



Photonic entangler






g g


s s


K. S. Choi, H. Deng, J. Laurat, H. J. Kimble. Nature 452, 67 (2008).


dark-state polariton

(Fleischhauer & Lukin, 2000)

Entanglement transfer

λ= 20%

Nature 452, 67 (2008)

Generation and characterization of N-partite state




~ 0 1

,,0 i−1

,1 i

,0 i +1

,,0 N

For example, a quadripartite W state –

Realization of ‘simple’ quantum systems

Exploration of quantum

complexities in multipartite states

ρ !

Characterization and verification of

entanglement for multipartite systems

Physical realization of strongly correlated system

Quantum interface for multipartite quantum networks

Goal: develop a dynamical quantum system,

capable of generating, storing multipartite

resources in quantum nodes and coherently

mapping them into quantum channels

(1) Measurement-induced entanglement for one

spin-wave excitation coherently shared among

four quantum memories

(2) Quantum-state transfers from entangled atomic

components to individual photonic channels

(3) Entanglement verification via quantum

uncertainty relations

K. S. Choi, A. Goban, S. B. Papp, S. J. van Enk, H. J. Kimble. Nature 468, 412 (2010)

Measurement-induced atomic W-state

Conditional atomic state upon a photoelectric detection at D h

Quantum numbers of spin-waves for given collective atomic modes

Quantum-state exchanges

Coherent mapping via dark-state polariton (Fleischhauer & Lukin, 2000)

Quantum-state mappings from individual components of atomic W-state to photonic

channels on a one-by-one basis (LOCC)



Superradiant emissions

Photonic W-state (generation) & verification

S. B. Papp*, K. S. Choi*, H. Deng, P. Lougovski, S. J. van Enk, H. J. Kimble

Science 324, 764 (2009)

1. W state input, Δ = 0 2. Separable state, Δ = 0.75



T -T

Uncertainty relation as signature of entanglement

Molmer and Sorenson PRL (2001) - CV

Hofmann and Takeuchi PRA (2004) -DV

Logouvski, van Enk, Choi et al. NJP (2008)


Δ= δ ˆM 2







Reck, Zeilinger, Bernstein,

Bertani PRL (1994)

Statistical measure of entanglement

Δ = δ ˆΠ 2

(and 3 other possibilities …)




Threshold for four-mode entanglement, calculate Δ for a state with at most 3 mode entanglement

∑ = 1− ˆΠi


For states containing

one excitation

Uncertainty relation as nonlocal, nonlinear witness

Contamination analysis for all possible less entangled, separable pure & mixed states

ˆρ ( p 0

, p 1

, p ) ≥2

= p 0 ˆρ 0

+ p 1 ˆρ 1

+ p ≥2 ˆρ ≥2

Critically, the distinction between


entangled and unentangled involves

vacuum and higher order statistics





Δ (3)



Δ (2)



Δ (1)


Normalized parameter

for contamination

y c

= 2 N −1 ⎞

N ⎠

⎟ p ≥2

p 0


p 1



0.0 0.5 1.0

y c

Lougovski, van Enk, Choi et al.

New J. Phys. 11, 063029 (2009)

genuine multipartite entanglement

(Guhne, Toth, Briegel, 2005)

= k-producibility

≠ n-separability

Parameters for genuine multipartite entanglement

For verification, two complementary measurements -

(1) y c - measurement (~ quantum statistics)

7! { (3)



(2) Δ - measurement (~ off-diagonal coherences)







= X i

h ˆ⇧ 2 i i hˆ⇧ i i 2

Parameter space for the multipartite entanglement

{0, 0} apple { ,y c } apple {0.75, 1}

Vol 468|18 November 2010|doi:10.1038/nature09568

Entanglement of spin waves among four quantum!


K. S. Choi 1 , A. Goban 1 , S. B. Papp 1 , S. J. van Enk 2 & H. J. Kimble 1

Nature 468, 412 (2010)

• Statistical behavior of heralded

atomic W-state:

• Quantum statistics y c and

coherence Δ of entangled

spin-waves tuned in tandem

In the low-excitation regime,

{ ,y c } ' {9⇠, 8⇠}

Statistical transitions of genuine

multipartite entanglement

delay = 200 ns




• Measurement-induced generation of atomic W-state

Dissipative dynamics of atomic W-state

Motional dephasing of spin-waves

W ' (1 3⇠)(cos2 ✓(⌧)|W ihW | + sin 2 ✓(⌧)ˆ⇢ (A)

n )+3⇠ ˆ⇢ (A)



Evolution of symmetric state into one-excitation subspace

containing subradiant excitation (i.e. vacuum component)

Temporal transitions of genuine multipartite entanglement

• Operational metric:

crossings of {Δ b


Δ b


Δ b



• Transiting from M-partite to

(M-1)-partite entangled states

Analysis via quantum uncertainty relations

• Analysis via quantum uncertainty relations

- Observations of statistical and dynamical transitions

- Minimum entanglement parameters

{ min ,yc min } = {0.07 +0.01 , 0.038 ± 0.006}


10 s.d. violation of Δ b


- Unconditional entanglement fidelity *

F (A) 0.9 ± 0.1

- Matter-light entanglement transfer

=0.38 ± 0.04

* Our analysis is based on the physical state

including vacuum as well as higher order

components, without relying on post-selection

Entanglement thermalization of quantum spin systems

Entanglement of spin-waves among four quantum memories

atomic pseudo-spins

Entanglement of four spins with infinite-range interaction

Entanglement thermalization of multipartite spin systems

Quantum uncertainty as a tool for quantum spin systems in thermal equilibrium


Raman excitations of spin waves

" Statistical transition of multipartite


Amico, Fazio, Osterloh & Vedral Rev. Mod. Phys. 80, 517 (2008)

Thermal excitations of spin waves

" Thermalization of multipartite


Quantum-enhanced phase estimation protocol

• Quantum measurements and metrology enabled by atomic W-states

e.g., precision metrology, quantum-limited measurements of magnetic fields, clock comparisons, etc.

1. W state input, Δ = 0 2. Separable state, Δ = 0.75


• Unambiguous quantum-state discrimination (USD)

Goal: find the random π-phase shifted ensemble (parameter)

in a single-measurement under the condition of =1

Four orthonormal W-states

detected via Δ

Ivanovic, I. D. How to differentiate between non-orthogonal states. Phys. Lett. A 123, 257–259 (1987).

Dieks, D. Overlap and distinguishability of quantum states. Phys. Lett. A 126, 303–306 (1988).

Peres, A. How to differentiate between non-orthogonal states. Phys. Lett. A 128, 19 (1988).

Quantum-enhanced phase estimation protocol

• Quantum measurements and metrology enabled by atomic W-states

• Physical implementation with random phase shifts in collective excitations

• Quantum benchmarks:

• Quantum-classical bound (with multimode coherent state)

• Upper bound for any separable states

Scaling behaviors for experimental physics

What’s inside here

Overwhelming technical complexity per each node

( > 20 stabilized lasers)

Collective effort of an ensemble of many people (as of late 2010)

Scaling behaviors for experimental complexities

What’s inside here

Name of the game:

Optical depth, coherence time

Small mode volume V m ,

Suppression internal and external states

Overwhelming technical complexity per each node

( > 20 stabilized lasers)

Advent of nano-device physics

Bring the atoms in proximity

of evanescent fields of a dielectric nanowire

Scalable quantum networks

with atoms, photons, and spins

Part 2 –

Atomic ensembles near nanophotonic structures


• “Optical Coherence and Quantum Optics” by L. Mandel and E. Wolf

• “Quantum Optics” by M.O. Scully and M.S. Zubairy

• “Atom-Photon Interactions” & “Photons and Atoms”

by C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg

• “Quantum physics in one dimensions” by T. Giamarchi

Review articles:

• B. Lounis and M. Orrit. Single photon sources. Rep. Prog. Phys. 68, 1129 (2005)

• H.J. Kimble, The quantum internet, Nature 453, 1023 (2008)

• A.I. Lvovsky, B.C. Sanders & W. Tittel, Optical quantum memory.

Nature Photon. 3, 706 (2009).

• K. Hammerer, A.S. Sorensen, E.S. Polzik, Quantum interface between light and matter

Rev. Mod. Phys. 82, 1041 (2010)

• N. Sangouard, C. Simon, H. de Riedmatten and N. Gisin,

Quantum repeaters based on atomic ensembles and linear optics,

Rev. Mod. Phys. 83, 33 (2011)

Rudimentary hybrid quantum networks

E. Togan et al. Nature 466, 730 (2010).

K. S. Choi, H. Deng, J. Laurat, H. J. Kimble. Nature 452, 67 (2008).

Transmission of quantum information between heterogeneous

elements via photonic quantum buses and coherent transfer

Photon bus

Quantum node A

Atomic ensembles B, C

dynamic electromagnetically

induced transparency

controlled generation of

photonic entanglement


spin qubit

g + e iφ A s → 10 γ + eiφ A 01 γ

Rudimentary hybrid quantum networks

Hybrid entangled state of

solid state and atomic qubits

Figure 13. Scanning


images [58] of mesa before

(a) after (b)nanocrystal has

been picked up with fiber

taper. Images of (c) fiber

taper and attached

nanocrystal aligned with

Atomic entanglement microdisk, (d) after and

placement. Imaging aided


coherent transfer to photonic


a white light source

and the into microdisk. the fiber taper



entanglement via evanescent

after crystal

image placement.

of microdisk

coupling of SiN x nanowires

E. Single-Photon Frequency Conversion for Interfacing Atoms and Color Centers The

cavities that form the basis of the photonic quantum circuits, described above are exceptional not

only in their ability to couple the atomic and NV center states to photons, but can also serve as

the nonlinear optical elements enabling photon frequency conversion and thus more directly and

resonantly linking the different emitters (atomic and solid-state) in our hybrid system, but further

allowing output signals at fiber-compatible telecommunications wavelengths, for robust, longdistance

transmission of quantum information. Thus, a central aim of QuMPASS will be to

develop techniques that allow an emitter to generate outgoing single photons of arbitrary

Diamond nanocrystal

frequency, enabling, e.g., hybrid networks connecting different types of emitters (atomic and



wavelengths (fiber-compatible telecommunications

Single wavelengths, atom for instance). implantation We have developed a novel scheme to accomplish this task using the

ultra-small mode volume of PC nanocavities, where the resonant single photon originating from

the emitter is frequency-converted using the nonlinearity of the cavity medium itself. This work

is in collaboration with Dr. D. E. Chang (a postdoctoral fellow at Caltech). Chang and Painter

have extended the original analysis based upon (2) processes to the case of (3) , as described in

the following section. We propose thereby to develop a powerful set of tools to coherently

convert optical frequencies from the bands relevant to diamond color centers to those resonant

Photonic crystal nanowire

“super” strong coupling 1

with narrow atomic transitions

E1. Single-Photon Frequency Conversion for Color Center to Atom Interfacing - Here we

propose a novel scheme for efficient wavelength conversion of single photons using the ultrasmall

mode volume of photonic crystal nanocavities, where the resonant single photon

Photon bus

NV diamond center, quantum dots

In collaboration with

Kerry Vahala and Oskar Painter (KNI Caltech)

EIT mapping

g 0

> κ,γ; Ng 0

>> κ,γ; C = Ng 0



Linear mapping: λ EIT



1 + C →1

Extreme quantum nonlinear optics


First observation of >= 10GHz vacuum

Rabi splitting in atoms: Reichel (LKB

CNRS), Esslinger (ETH)

Optimal control theory for efficient EIT:

Gorshkov et. al. PRA 76, 033804 (2007)


the fiber Integrated and spaced along quantum the red-detuned nano-devices standing-wave by red for 2 QIS . Two sets of trapping wells

extend along the z-axis separated by an azimuthal angle of . For the case of linear polarization

Quantum parallel to interface the x-axis between for


, atoms, Fig. 5(b) photons, displays the potential U

trap Projected

in the x nano-fiber

z plane, with the

set and of trap phonons minima (Oskar shown Painter’s along the group) axis of the fiber.

magic atom trap

With “Extreme” modest input nonlinear powers quantum ~ 40mW, optics trap depths ~1mK

should be readily achievable.

QuMPASS: Quantum Memories in Photon Atomic Solid-State Systems

Figure 5. An optical trap U

trap for Cesium atoms around

a nano-fiber, which is indicated by the gray shaded

region. U

trap is generated by two evanescent fields that

provide 3-dimensional confinement for the trapped atoms

outside the 500 nm diameter optical fiber, shown in (a)

the x y plane, and in (b) the plane. Specifically, U


results from two counter-propagating red-detuned beams,

and a blue-detuned beam in a so-

configuration [29], as shown in the inset. The standing

wave structure of the attractive red-detuned fields and the

repulsive force from the blue-detuned beam enable

trapping of single atoms at each node of U

trap near the

dielectric waveguide despite the strong attraction from

440 nm

van der Waals forces from the surface.

.3 !0.2 !0.1 0

igure 4. An atomic ensemble

torage and retrieval of quantum optical fields to/from collective spin excitations.

More specifically, as illustrated in Fig. 4 an important goal of the QuMPASS program is

n D). Our goal is to achieve

he efficient transfer of quantum states of light (including multipartite entanglement) to and from

ollective spin excitations in multiple atomic memories. The critical quantum interface that will

erve to link atomic and solid state systems is described in Section B.

The storage and readout of a memory element will be achieved deterministically by

apping of quantum states of light into and out of the trapped atomic ensemble via

lectromagnetically induced transparency (EIT) [26-28]. State mapping by way of EIT is by now

ell developed for conventional setups in AMO physics, beginning with the demonstration of

he storage and retrieval of classical pulses to and from an ensemble in 2001 [29,30] and

xtending into the quantum regime of single photons in 2005 [31,32]. As previously discussed,

n 2008 the Kimble group achieved the reversible mapping of photonic entanglement into and

ut of pairs of quantum memories by the EIT process [4].

Vetsch To et enable al. Phys. on-chip Rev. quantum Lett. 104, memories 203603 with (2010) atomic ensembles in QuMPASS, we will

ursue State-insensitive the following research nanofiber objectives: trap. In preparation. Phys. Rev. Lett. (2012)

We achieved trapping times for Cesium atoms of

= 50ms in a two-color trap with wavelengths



nm and blue

780 nm. Moreover, for two

parallel chains with total atom number N=2000, the

authors observe an optical depth = 8, corresponding to

an average absorbance per atom of = 0.65%.Inspired

by this work, we have investigated trap designs that

mitigate some problems for earlier implementations [35].

Namely, the excited states of the 6P32

manifold are not

1D atomic array in a state-insensitive nanofiber trap

What’s inside here

• Array of ~1000 Cs atoms trapped by the near fields of nanofiber

• Utilize confinement of EM field with low dimensionality to

enhance matter-light interaction

• A new type of strong coupling between single photons and atoms


times for Cesium atoms of

r trap with wavelengths

80 nm. Moreover, for two

tom number N=2000, the

pth = 8, corresponding to

tom of = 0.65%.Inspired

estigated trap designs that

arlier implementations [35].

f the 6P

32 manifold are not

each node of U

trap near the

e the strong attraction from

e surface.

the plane. Specifically, U


pagating red-detuned beams,

in a so-

n in the inset. The standing

ive red-detuned fields and the

blue-detuned beam enable




A state-insensitive nanofiber trap


optical potential




Photon transport in 1D spin array

U trap





Cs atom

Trap depth ~500 µK

(at ~150 nm from surface)


U trap









optical potential



0 200 400 600 800


surface interaction

(vdW-CP crossover)


0 200 400 600 800


Two-level atom w/ transition frequen

|e⟩ |e⟩


Two-level Two-level atom Optical w/


atom transition w/ dipole transition frequency |e⟩


I (a.


u. frequency ) + Optical ω

ω field at frequency ω

Red-detuned Gaussian |e⟩ beam:


ω ω








Dipole force:

F dipole ∝ α ∇I

Two-level Orders atom w/ of magnitudes:

transition frequency ω

+ Optical Two-level ω+ Optical field at atom frequency field at w/ frequency ωtransition ωfrequency AC electric ω field E |g⟩

+ Optical AC


electric field field

atom + Optical Na: field w/10µm at frequency waist, induces ω

at frequency E induces

w/ transition





650GHz an det., Dielet elec

AC electric ω field ω

E induces an electric dipole AC moment electric 220mW field d power E moment induces => 7mK an d electric deep trap dipol

Two-level + Optical ω

|e⟩ AC Two-level electric atom field + off-resonant at frequency optical ωfield

atom field w/ E induces transition an frequency electric Rb: ω

dipole w/10µm moment waist, 80nm d d = det.,


α E

AC electric d = field α E induces

+ Optical field at frequency d E induces = ωα an


electric an 1 electric W



moment dipole => 6mK d moment = deep α E trap d

AC electric field E


induces d = an α E electric dipole moment d

Dieletric material: caracterized |g⟩ by susceptibility Dieletric Dieletric r , material: with material: caracterized caracterized by susceptibili by Dieletric material: caracterized d by = susceptibility α Dipole E potential: , with


Dielectric characterized d = α by E susceptibility

Dieletric material: caracterized by V dipole = function −d ∙, E with

−α E

P = ε 2


0 χ E

P = ε 0 χ E


Dieletric material:

Dieletric material: caracterized

P caracterized = ε 0 χ


E Vby susceptibility dipole susceptibility ∝ α I , with

, with

Dipole potential:

Far-detuned Dipole potential: Potential: P = ε 0 χ E

Far-detuned Potential:


Dipole potential: P = ε 0 χ E Dipole force:


dipole = −d ∙ E = −α E

of 2 beams V P = ε

free-space V = −d dipole ∙ E = −αtraps

0 χ E

V V dipole E(a. 2 u. F)

V dipole ∝ α I

dipole ≈ ħΓ2 I(r)

ctive potential for 0, ie blue-detuned beams

Dipole force:


Dipole force: micro-spheres,

∆= ω

micro-spheres, is max. at

L − ω at

Optical lattices

∆= ω L − ω at


neutral manipulate microspheres, neutral Dipole atoms, force: DNA …

Counterpropagating fields

neutral dipole = −d ∙ E = −α E

atoms, beam DNA…

2 beams

V waist.


dipole ∝ α I

Silica microspheres in

dipole ≈ ħΓ2 I(r)

Attractive dipole ∝ α ∇I


potential for 0, ie blue-detuned beams holographic optical tweezers

IQIM 12/09/2011

IQIM 12/09/2011 7

IQIM 12/09/2011 7

IQIM 12/09/2011 4πc 2

Silica microspheres


in optical tweezers

A. Ashkin et al. Opt. Lett. 11 (5) 288-290 (1986)

Grier, Nature 424, pp.810, (2003)

IQIM 12/09/2011 9

IQIM 12/09/2011 11

Observation of a single-beam gradient force optical trap for dielectric particles

Ashkin et al. Optics Lett. 11, 288 (1986)

A revolution in optical manipulation.

Grier, Nature 424, 810 (2003)

P = ε 0 χ E

Counter-propagating beams (optical lattices):

∆= IQIM ω12/09/2011

L − ω at

IQIM 12/09/2011 9

I sat = ħω at 3 Γ

IQIM 12/09/2011 10


I sat


Differential scalar shift in optical transition

• Optical lattices: cavity QED, optical clocks,

ultra-cold atoms • Optical lattices: cavity QED, optical c

What happens to the transition frequency

ultra-cold atoms

• Optical lattices: cavity QED, optical clocks, ultracold atoms

Examples of free-space dipole




ω probe ~ω at (atomic clock, optical pumping…)


-space dipole traps

Bloch, Nature Phys. 1, 23 (2005).

y QED, optical clocks,

• Evanescent surface traps




Differential shift

If V dipole

|e⟩ ≠ V dipole


Differential shift of the

transition frequency

h∆ν = V dipole

|e⟩ − V dipole


Bloch, Broadening

Nature Phys. 1, pp. 23, (2005)

IQIM 12/09/2011 12

Differential shift of the


For two-level atom,

V dipole

|e⟩ = −V dipole


IQIM 12/09/2011

Bloch, Nature P


Single atom microscope (Greiner, 2010)

Multi-level Multi-level atoms atoms

Light shift of multilevel structure

Multi-level atoms

Cs ground state


In general, In general,

In general, V dipole ω, V

|i⟩ =

dipole ω, −d|i⟩ ω, =


−d∙ E ω, |i⟩ ∙ E

= −α ω, =


−αE ω, 2

|i⟩ E 2

Polarizability: Polarizability:

In general,

V dipole ω, |i⟩ = −d ω, |i⟩ ∙ E

= −α ω, |i⟩ E 2

Atomic dynamic polarizability


For detunings


For detunings large



to the hyperfine structure

large compared to the to the

Ground hyperfine state hyperfine light structure. shift: structure.

Ground-state light shift

For detunings large compared to the

hyperfine structure.

V dipole = 3πε 0c 3



3ω 1


Γ 1

+ 2

Δ 1

Cs ground state

Γ 2


2 Δ 2

E 2


D 2

D 1


IQIM 12/09/2011 16

IQIM 12/09/2011 16

IQIM 12/09/2011

Multi-level Magic Multi-level atoms

wavelength conditions atoms


In general, In general,

In general, V dipole ω, V

|i⟩ =

dipole ω, −d|i⟩ ω, =


−d∙ E ω, |i⟩ ∙ E

= −α ω, =


−αE ω, 2

|i⟩ E 2

Polarizability: Polarizability:

Atomic dynamic polarizability

Cs ground state


For detunings


For detunings large



to the hyperfine structure

large compared to the to the

Ground hyperfine state hyperfine light structure. shift: structure.

Ground-state light shift

V dipole = 3πε 0c 3

Excited state

Ground state

Cs excited state 6P 3/2



3ω 1


Γ 1

+ 2

Δ 1 3ω



Γ 2

Δ 2

E 2

Magic wavelengths

No differential light shift

Trapped excited state

IQIM 12/09/2011 16

IQIM 12/09/2011

an effective lifetime of

State-insensitive traps in free-space

tion and communication [7–12].

downwards by comparable amounts, 6S 1=2

’ 6P3=2

, albeit

In this Letter we present experiments to enable quantum

information processing in cavity QED by (1) achiev-

The task then is to achieve state-independent trapping

with small dependence on 100 F 0 ;m s [18]. F

0 for Experimentally, the shifts 6P 3=2


however, the attainable line Q factor will be limited by

the collision-limited lifetime of 10 s at the vacuum pressurestill

of 10maintaining torr and/orstrong by the mean coupling photon-scattering for the 6S 1=2 !

ing extended trapping times for single atoms in a cavity while

while still


maintaining strong coupling,






a 6Ptime 3=2 of

transition. ( Single 10 s) of atoms Atoms

Our experimental in a far-off-resonant in an Optical

setuplight to achieve trap. Cavity


trapping potential for the center-of-mass motion that is end is Figure schematically 2 shows the depicted light shift for in Fig. the 2 [2]. Significantly,

largely independent


of the internal


atomicBoozer, state, and


(3) the cavity


has aStamper-Kurn, TEM 00 longitudinal


1 S 0 and 3 P 0 states

as a function of the trapping laser wavelength mode located with an nine

demonstrating a scheme that allows continuous Phys. Rev. observation

of trapped atoms by way of the atom-field coupling.

Lett. 90, intensity 133602 of I (2003) 10 kW=cm 2 . The calculation is performed

by summing up the light shift contributions

with electronic states up to n 11 orbits [11],

PHYSICAL REVIEW LETTERS weekin ending which

More specifically, VOLUMEwe 90, have NUMBER recorded 13 trapping times up to 0.0

we employed 4 APRIL 2003


new values of the dipole moments determined

in recent

3sfor single Cs atoms stored in an intracavity far-off

resonance trap (FORT) [13], which represents an improvement

by a factor of 10 2 L 800 nm. The light shifts around the


gradient cooling

-1 experiments 6S 1/2 [15] to find the intersection

[13]. Freely falling atoms arrive at the


wavelength at

cavity mode over an interval of about 10 ms, with kinetic

beyond the first realization intersection are mainly determined by the states indicated

in Fig. 1(a): The 6Plight transit time t 2w 0 =v 3/2

energy E K =k B ’ 0:8 mK, velocity v ’ 0:30 m=s, and

of trapping in cavity QED [2], and by roughly 10 4 -2


shift of the 3 P

’ 150 s. Two additional 0 state can be

FIG. 1. Simplified optical coupling scheme for 87 Sr. (a) In the


‘‘pushed pairs downward’’ of counterpropagating beams in a

prior results for atomic trapping [3] and localization [4] -0.5 tuned arbitrarily in the near infrared range, λ F (nm) being

limit of large detunings i of the coupling laser compared to

with n ’ 1 photon. We have also continuously monitored configuration 925 by 3 S

illuminate the 1 and

region 935 ‘‘pulled upward’’ by

the hyperfine splittings hfs, the squared transition dipole

between the cav-94ity

mirrors 1 state, while that of the 1 S

moment of the upper J manifold can be simply added up,

the 3 D

along directions at 45 0 state monotonically

trapped atoms by way of strong coupling to a probe beam,

relative to ^y; ^z (the

resulting in a quasiscalar light shift. (b) 3D optical lattice decreases toward the dc Stark shift. This tuning mechanism,


including observations ‘‘y z beams’’) and contain cooling light tuned red of

provides Lamb-Dicke of trap confinement loss atomwhile by itatom prevents over atomatom

1s. interactions. These measurements incorporate auxili-


F 4 ! F 0 can be similarly applied to heavier

5 and repumping light near the F 3 !

intervals ’

F 0

atoms. At L, the light shift ac

-1.0 3 transition [20]. These beams eliminate the freefalary

cooling beams, and provide the first realization of changes with the trapping laser frequency ! as

FIG. 2 (color online). Schematic of experiment for trapping d

velocity to capture atoms in the FORTand provide for

cooling forsingle trapped



in an optical


cavity in


a regime of

tostrong a cavity.

coupling. subsequent ac =d! 3:6 10 10 and 1:3 10 9 for the 1 S

hyperpolarizabilities of the upper and lower states, which

cooling of trapped atoms.



Our protocols Relevant are facilitated cavity parameters by thearechoice length of l a 43:0 ‘‘magic’’

3 P

in the general case depends both on the light wave m, waist fre-

for 0 the 23:9 ! FORT and m, and on[14–16], finesse the unit F polarization for 4:2which 10 5 atvector the 852 relevant nm. e. The Higher-

inset time for single trapped atoms in our FORT: (1) Trapping F'

We employed 0 states, respectively. This precision enhancement

of more than

two distinct protocols to study the life-

-4a factor of -210 9 allows0 one to control 2 the light 4 m

wavelengthwquency shift well within 1 mHz by defining the coupling laser

illustrates transverse beams used for cooling and repumping.

atomic levels order arecorrections shifted almost are included equally, in the thereby hyperpolarizability providing

significant advantages for coherent state manipulation



the dark

1 MHz





atom illuminated only by the FORT

FIG. laser 1 (color at F and online). 8 precision for the optical

the cavity-locking ac-Stark shifts laser at ^ frequency,

e;! and in the higher-order multipole corrections to

C. For this

6S1=2 ; ^ 6P 3=2

for the

which can be easily accomplished by conventional optical

6Sprotocol, 1=2 ; 6P 3=2 strong levels coupling Cs enables for a linearly real-time polarized monitoring FORT. of The

of the Ultrastable

the polarizability

atom-cavity mode orders system. Optical



dipolewith M1 andNeutral electric quadrupole

E2 terms in addition to the electric-dipole polar-

the cavity for initial triggering of

Atoms frequency in an synthesis

below the mode employed for cavity QED at inset single shows atoms^ Engineered


within ; ^ techniques. Using Light the same Shift set Trap of

A major852 obstacle nm, at to the the wavelength integration F of 935:6 a conventional

dipole moments 6P 3=2 ;F 0 4 as functions of wavelength F .

nm, allowing the The cooling full plot light gives and ^ as used in the above calculation, the

izability E1 ): Katori, Takamoto, Palchikov, Ovsiannikov for 6P 3=2

final versus detection. m F 0 for(2) each Trapping of the levels with 6P 3=2 ,

red-detunedimplementation FORT within of athe FORT setting with of 6S1=2 cavity ’ 6P3=2 QED . Theisfield

F 0 blackbody frequency shift [19] in the clock transition is

continuous 2; 3; 4; 5observation for of single atoms with cavity probe

F 935:6 nm. In each case, the normalization

and cooling is ^ (2003)

that excitedto electronic excite e;! this states cavity mode generally is provided


experience byRev. a laserLett. a pos-


91, 173005


E1 e;! M1 e;!

PHYSICAL E2 e;! : (2)

REVIEW LETTERSlight = during the trapping week ending interval. In this

6S1=2 F 935:6 nm .


which is independently

91, NUMBER 17

24 OCTOBER 2003

locked to the cavity. The finesse of case, atoms in the cavity mode are monitored by way of

By canceling out the polarizabilities of the upper and

the cavity at F is F 2200 [17], so that a mode-amatched 0031-9007=03=90(13)=133602(4)$20.00 input power of 1:2 mW gives a peak ac-Starkhowever, © auxiliary 2003 the attainable The y American z beams.

effective the cavity lifetime probe of beam, 100 s with [18]. cooling Experimentally, provided by the

lower states to set e;! 0, the observed atomic

133602-1 transition frequency will be equal to the unperturbed

line Q factor Physical will be Society limited by 133602-1

shift 6S 1=2

=2 47 MHz for all states in the 6S 1=2 the collision-limited (1) In our first lifetime protocol, of 10the s at Fthe vacuum 4 ! F 0 pressure

of is strongly 10 10 torrcoupled and/or by to the mean cavityphoton-scattering

field, with zero detuning

5 transition









a trap






0 =k B


I /jEj

mK, 2 ,


as long





for all experiments.

corrections O E 4 aretime of ( 10 thes) of cavity atomsfrom in a far-off-resonant the bare atomic lightresonance,




Principal parameters relevant to cavity QED with the Figure ! 2 shows C ! the light 4!5 0. Inshift contrast for theto 1 SRef. 0 and[2], 3 P 0 states here the FORT


We first

in Fig.


2 are




Rabi frequency

of the



0 for a single

as a function of the trapping laser wavelength with an

is ON continuously without switching, which makes a

intensity of I 10 kW=cm



of excitation E1 e;!











cooling mechanism necessary 2 . The calculation is performed

by summing up the light shift contributions

to load atoms into the trap.


; due to cavity

In order











with The electronic initial states detection up to n of 11 a single-atom orbits [11], in falling which into the


For our




g 0 =2


24 MHz,



by the

we employed cavity mode new values is performed of the dipole with the moments probedeter-

inlower recent sideband experiments of [15] the vacuum-Rabi to find the intersection spectrum (

beam tuned to



MHz, and

! that


is the most

2:6 MHz,




g 0 is for



6S 1=2 ;F 4;m F 4 ! 6P 3=2 ;F 0 5;m 0 p

in experimental physics. Other parameters such

F 4




wavelength ! p ! at 4!5 L 8002 nm. The 20 MHz). light shifts Thearound resulting the increase

light polarization

in atomic Cs




0 852:4

have less



Strong coupling

on theintersection transmitted are mainly probe determined power when by thean states atomindi-

catedregion in Fig. of 1(a): optimal The light coupling shift of[21,22] the 3 P 0 triggers state canON be

approaches a








is to employ

0 ; ], resulting

the J 0





FIG. 1. Simplified optical coupling scheme a pulse of

photon exhibitsand a scalar atom numbers light shift n [9]. 2 for

0 = Here 2g 2 87 we

0 ’ Sr. 0:006, (a) propose In the

N thetuned 0 transverse arbitrarilycooling the light near from infrared the range, y z beams, being

limit of detuned

2 =g 2 large detunings i of the coupling laser compared to


0 ’ 0:04. The small transition shifts for our FORT

‘‘pushed downward’’ by

41 MHz red of ! 3 S 1 and ‘‘pulled upward’’ by

the 21 S

hyperfine 0 ! 5s5p


3 P 0 forbidden transition (

hfs, the squared transition 0 698 nm)


4!5 . During the subsequent trapping


mean ofmoment 87 Srthat with of gthe nuclear

0 is upper considerably Jspin manifold I 9=2 can larger be as simply the than‘‘clock’’ the addedspatially

up, transition

resulting [9], inshift awhich quasiscalar we

3 DFIG. interval, 1 state, 2. while Light that shiftofas the a function

all near-resonant 1 S

fields 0 stateof monotonically

the trapping laser wavelength

for a laser intensity of I 10 kW=cm 2 . The solid and

decreases toward the dc Stark shift. This





dashed therefore, transverse linescan showbecooling the similarly lightlight). shifts applied After for the toa variable heavier

1 S and 3 delay P states, t T

OFF (includ-

dependent 0 of take the light bare shift. advantage atomic (b) 3D of optical frequency the lattice hyperfine em-nism, ,

3 1;3

k 0 0

TE 01


– A significant part of the energy propagates in the

Evanescent HE 11


wave 11 HE

evanescent field outside for 11 fundamental mode of nanofibers

EH 11

the fiber. EH 11

EH 11

TM TM 01

HE 31 01



Scanning Electron Microscope 31 Image

HE 21

TM HE 2101 HE Fiber dispersion


0 1 2 3 4 5

n 12


n 2 HE 12 n 2

HE 21 n n n 2


1 1

0 1 0 n 2 1 3 2 4 3 5 4 5 HE 12 n 2

=1064 nm

0 1 2 3 4 5

V = 2 a nV 2 = a n 2 1 n 2 1 n 2 P=2.2mW



V = 2 a n 2 1 n 2 a=250nm



Figure 1. Normalized Figure 1. Normalized propagation propagation constant /k constant 0 versus V/k parameter 0 versus Vfor parameter the first for /kthe first out =60%

0 TE 01

seven modes seven in the modes fibre. inThe thedashed fibre. The vertical dashed linevertical is located lineat isV located = 3.11atwhich

V = 3.11 which HE

Figure 1. Normalized propagation constant /k

corresponds to the three trapping configurations considered in 0 versus V parameter for 11

the first

corresponds to the three trapping configurations considered in this paper. this paper.

EH 11

seven modes in the fibre. The dashed vertical line is located at V = 3.11 which

Evanescent Field


corresponds to the three trapping configurations considered in this paper.





HE 21

The fundamental 2.2. The fundamental HE 11 modeHE with 11 quasi-linear mode with quasi-linear polarization polarization HE 11 mode

n 2 25

HE 12 n 2

E = A(r) + A 0 1 2 3 “Quasi-linear” 4 5E (r) cos 2φ exp i ωt − βz

x > E y ,E z

EE fieldThe equations EE fieldof equations the fundamental of the fundamental HE 11 modeHE with 11 mode quasi-linear with quasi-linear polarization polarization outside the outside the

fibre, 2.2. Fundamental

i.e. for The r > fundamental a, are


given by HE[7]

E = B(r) sin 2φ exp i ωt − βz

, i.e. for r > a, are given by [7] 11 of mode the with waveguide quasi-linear polarization

V = 2 a n 2 1 n 2 2

E = i C(r) cos φ exp i ωt − βz

11 J 1 (h 11 a)

E x (r,

The 11

, z,



field J

= 1 (h

A 11 equations a)

, , z, t) = A 11

2q 11 K 1 (q 11 a) [(1 s 11 11)K 0 (q 11 r) cos(' 0 )

2q =937nm

11 K 1 (q 11 a) [(1 s of the fundamental HE

11)K 0 (q 11 r) cos(' 0 ) 11 mode with quasi-linear Figure polarization 1. Normalized outside propagation the constant /k 0 versus V paramet

fibre, i.e. for r > a, are given by [7]

seven modes in the fibre. The dashed vertical line is located at V =

+ (1+s a=250nm

+ (1+s 11 )K 2 (q 11 r) 11 cos(2 )K 2 (q 11 r) ' cos(2 0 )] exp[i(!t ' 0 )] exp[i(!t 11z)], 11z)], (1) corresponds (1) to the three trapping configurations considered in this

11 J 1 (h 11 a)

E x (r, , z, t) = A 11


11 J 11 J 1 (h 11 K

11 a) 1 (q 11 a) [(1 s 11)K 0 (q 11 r) cos(' 0 )

, , z, t) E y = (r, A , z, t) = 1 (h

A 11 a)


2q 11 K 1 (q 11 a) [(1 s 11 11)K 0 (q 11 r) sin(' )

2q 11 K 1 (q 11 a) [(1 s 2.2. The fundamental HE 11 mode with quasi-linear polarization

+ (1+s 11)K )K 0 (q 211 (q r) sin(' r) cos(2 0 ) ' 0 )] exp[i(!t 11z)], (1)

The EE field equations of the fundamental HE 11 mode with quasi-linear polarizatio

+ (1+s 11 )K+ 2 (q (1+s 11 r) 11 sin(2 )K 2 (q 11 r) ' 0 sin(2 )] exp[i(!t ' 0 )] exp[i(!t 11z)], 11z)], fibre, i.e. for (2) r > a, are given (2) by [7]

Input polarization

11 J 1 (h 11 a)

E y (r, , z, t) = A 11

J 1 (h 11 a) J 1 (h 11 a)

, , z, t) E z = (r, iA, z, t) = iA 11

K 1 (q 11 a) K 11 1(q 11 r) cos( ' 0 ) exp[i(!t 11z)], (3)

K 1 (q 11 a) K 2q

1(q 11 r) cos( 11 K 1 (q

' 11 a) [(1 s 11 J 1 (h 11 a)

11)K 0 (q 11 r) sin('

E 0 ) x (r, , z, t) = A 11

2q 11 K 1 (q 11 a) [(1 s 11)K 0 (q 11 r) cos(' 0 )

0 ) exp[i(!t 11z)], (3) + (1+s 11 )K 2 (q 11 r) cos(2 ' 0 )] exp[i(!t 11z)],

+ (1+s 11 )K 2 (q 11 r) sin(2 ' 0 )] exp[i(!t 11z)], (2)

e where

apple apple apple apple


s 11 =

(h 11 a) + J1 0(h 11a)

2 (q 11 a) 2 h aJ 1 (h 11 a) + K1 0(q 1



s 11 =

, (4)

(h 11 a) + 1 J1 0(h 11a)

2 (q 11 a) 2 h 11 aJ 1 (h 11 a) + K1 0 11 J 1 (h 11 a)

(q 1 E y (r, , z, t) = A 11

J 1 (h 11 a)


, (4)

E z (r, , z, t) = iA 11 q 11 aK 1 (q 11 a) q 11 aK 1 (q 11 a)

q q K 1 (q 11 a) K 2q 11 K 1 (q 11 a) [(1 s 11)K 0 (q 11 r) sin(' 0 )

1(q 11 r) cos( ' 0 ) exp[i(!t 11z)], + (1+s 11 )K 2 (q 11 r) sin(2 (3) ' 0 )] exp[i(!t 11z)],


h 11 = k0 2n2 2

h 11 = k0 2n2 2


1 11 , 1 11 , (5) J (5) 1 (h 11 a)

q q






q q 11 =


k0 2 11 =


k0 2n2 s

2 . 11 = n2 2

(h . (6) (6)

11 a) + 1 J1 0(h E z (r,


2 (q 11 a) 2 h 11 aJ 1 (h 11 a) + K1 0 , (q z, t) A = significant iA 11

K 11a) 1 (q 11 a)

part K 1(qof 11 r) the cos( energy ' 0 ) exp[i(!t propagates 11z)], in

Decay length: 100 – 300 nm (a~ 200 where nm)

the evanescent , field (4) outside the fiber.

q 11 aK 1 (q 11 a) apple The apple





J1 0(h scale ~

11a) K1 0(q 1


Two-color evanescent fiber trap

Two-color Optical Trap in a TOF

r Optical Trap in a TOF


nsity is maximal Balykin @ fiber-surface et al., PRA => cannot 70, 011401(R) use single (2004) freq.

o-colour FORT:

First experimental demonstration:

Red detuned beam => attractive potential.

Vetsch et al., PRL 104, 203603 (2010)

Blue detuned beam => repulsive potential.

Choose the right ratio P blue /P red to confine the atoms radially.

Optical Interface Created by Laser-Cooled Atoms Trapped

3D confinement

in the Evanescent Advantages: provided


by choice


of polarizations

an Optical

+ reddetuned



Vetsch et al., Phys. Rev. Lett. 104, 203603 (2010)






- High OD (good candidate for Q memory)

- 1D atom-chain

U blue


- Lengthscale red

(integration in micro/nano devices)



Two-color FORT

The atoms interact with the

evanescent field of the subwavelength


- FORT shifts caused by the evanescent field intensity + polarization

U red

N at 2000

lifetime 50ms

IQIM 12/09/2011

Linewidth ~ 20 MHz

Frequency shift ~ 13 MHz

Optical depth ~ 13

• State sensitive optical trap

• Untrapped excited state

• Ground-state decoherence

IQIM 12/09/2011



P red =2*2.2mW


P blue =25mW


Strong guiding regime:

Evanescent F


HE 11 mode

E = A(r) + A (r) cos 2φ exp i ωt − βz

E = B(r) sin 2φ exp i ωt − βz

E = i C(r) cos φ exp i ωt − βz

Non-transverse fields

ye Cesium. dipole considering where d the is the Hamiltonian electric dipole for an operator atom interacting and E is with electric an electric field operator. field Taking

ipole here

into account the atomic hyperfine structure, this Hamiltonian decomposed


into ˆd



quality y 1

where is account the ˆd

We show that the light shifts caused by the elliptically polarized components

|2 |E

micro-cavities y 1 |2 cause significant

electricbased A the state-insensitive,

dipole on

atomic operator optically heating of

hyperfineand trapped a trapped

structure, Ê isatoms.

atom [29]. This situation can be remedied by the

is of the theelectric two circular dipole modes operator on the x-zand plane


the Êthis f .

|E electric is Hamiltonian the electric field operator.

nanofiber can field operator. decomposed Taking

trap Taking

of the y

1 |2 +|E

fiber’s y


into |2 use evanescent itsof spherical “magic”


tensor components parameterized by the dynamic polarizability ↵(!)

into account account its the spherical atomic the tensor atomic hyperfine Ĥ

field wavelengths ls hyperfine =


structure, ˆd

not for

· Ê,

negligible. which ↵ (0)

parameterized this Hamiltonian

|gi We

structure, this by = then

the Hamiltonian ↵(0) |ei

[30, propose 31, 32, a34].

dynamic can bepolarizability decomposed can(1)

scheme to cancel

Explicitly, the spherical components of the beams E be decomposed ↵(!)

nsensitive nto


itsLight [40, Hamiltonian: 41, 42]:

[40, spherical



nanofiber and

42]: tensor

The generate trap components


Ĥ a

ls =

term two-color,

into its spherical tensor components

ˆd parameterized Ĥ1 · Ê,

of Eq. state-insensitive, (2) 4 (fw,bw)

i (in the rotated basis) are given by



the dynamic

a Zeeman-like three-dimensional

polarizability (1) splitting


trap proportional for Cs to a

parameterized by the dynamic polarizability ↵(!)


ˆd atoms is41, the


42]: along electric projection the dipole nanofiber. operator the total andatomic Ê is the angular electric momentum field operator. F and arises Taking from a so-called “fictitious

, [40, 41, decomposition:

42]: Ĥ

the electric dipole operator ls =

and Ĥ0 +

Ê Ĥ1 +

count we discuss the atomic an ab initio


magnetic (fw,bw),y


Ĥhyperfine Ĥ2




= field” Ĥ0 + structure, proportional electric field operator. Taking

= Ĥ1 + of

nt the atomic hyperfine structure, (0) Ĥ2 thethis optical toHamiltonian the nanofiber ellipticity trap canof for be the atomic decomposed electric field [36]. In the case of a

how Ê

this ( ) · Ê

spherical that • Scalar the tensor Ĥlight ↵ (0) Ê ( ) · Ê (+) Hamiltonian (+)

ls = Ĥ0 + Ĥ1 !

2.1. ac Stark

free-space shift: components shifts E

shift (fw,bw),y




Ĥ can be decomposed

ls =

(1) (Ê(

erical tensor components parameterized +i↵ ) ⇥Ê (+) )·ˆF


= ↵ (0) Ê +i↵ ( Ĥ0 + parameterized by the elliptically Use ) (1) · (Ê( (+) Ĥ1 + by the polarized of red-detuned

dynamic polarizability components and blue-detuned magic wavelengths



plane wave 2q 11

[(1propagating s 11 )K 0 (q 11 along r)+(1+s the z 11 axis, )K 2 (q Ĥ 111 r)] can± ↵(!) be K 1 expressed q 11 r in terms (C.5) of the


(687 nm, 937 nm)


by F the dynamic polarizability ↵(!)


+ P ⇥Ê

, evanescent 42]: fieldStokes are E not (fw,bw),y operators negligible. (+) )·ˆF


↵ (2) Ê µ ( ) Ê ⌫

(+) 3 1

( ˆF F (2F 1) 2 µ ˆF⌫ + ˆF 1

⌫ ˆFµ ) ˆF



= F

P ↵ (0) Ê ( Ŝ 11

) =(Ŝ0, We · Ê (+) then Ŝx, Ŝy, propose Ŝz) as[41]: a scheme to cancel

i, 1 2q 11

[(1 s 11 )K 0 (q 11 r)+(1+s 11 )K 2 (q 11 r)] ⇧ K 1 q 11 r,

ndWe generate start by a two-color, considering h

↵ (2) Ê ( )

2 3 µ⌫ ,

µ Ê ⌫

3 1

( ˆF µ,⌫ F (2F 1) 2 µ ˆF⌫ + ˆF 1

⌫ ˆFµ ) ˆF


(1) (Ê(


state-insensitive, ) ⇥Ê the (+) Hamiltonian )·ˆF three-dimensional for Fictitious an atom magnetic interacting trap for Cs with an 2 (2) electric field


3 µ⌫ ,


Ĥ ls = Ĥ0 + + P (1) (Ê(

+i↵ ) ⇥Ê (+) )·ˆF


Ĥ1 + ↵ (2) Ê Ĥ2 µ ( ) Ê (+) 3 1

( ˆF

where = ↵ (0) where (0) Ê , ( ↵ (1) ) µ,⌫

↵ · (0) and Ê

, (+)

↵ (1) (2) and are ↵ the (2) F (2F 1) 2 µ ˆF⌫ + ˆF 1

⌫ ˆFµ ) ˆF



he Ĥ ls = Ĥ0 + Ĥ1 + = Ĥ2 !


• Vector shift:

in the dipole approximation: F

2 3 µ⌫ ,

+ P hĤ ↵ (2) Ê µ ( ) Ê (+) 3 1

scalar, are thevector scalar, and vector ( ˆF F (2F 1) 2 µ ˆF⌫ +

tensor andatomic tensor ˆF 1

⌫ ˆFµ )

dynamic atomic ˆF


= ↵ (0) Ê ( ) · Ê (+)

1 / ↵ (1) (!)✏ ˆF



where we find the relationship between the circular components (q = ±1) z

F , of forward and


backward beams g

2 broadening


with E (fw,bw),y

3 µ⌫ ,

i,±1 = E (bw,fw),y

dynamic polarizabilities, polarizabilities,

here ↵ Ê (0) (+) and Ê (+) (1) (Ê( i,⇧1 , thereby ⌅ (fw) = ⌅ (bw) . Thus, we can compensate for the vector shift



Ê ( ) (Ê(


, (1) and ↵ ⇥Ê are (2) Ê ( (+)

are the )·ˆF



+i↵ ) ⇥Ê (+) )·ˆF

shift Hamiltonian




are positive scalar,

the positive and vector negative and

and tensor

negative frequency atomic

frequency components dynamic



of the (2) electric of thefield,

electric field,

(+) where ˆF =


and Ê

+ ( P Î ↵ + ) ˆF P h ls = ˆd · Ê, (2)


where ✏ = hŜzi/hŜ0i = |E vector

+1| 2 |E 1 | 2


( (1) (w (fw) ) (1) (w (bw) F

Inherent )) ˆ y

property (0)

are Ĵ, = is ↵ (1) Î (2) the + and Ê Ĵµ ( atomic is )

↵ Ê the atomic totalh

angular total

↵ (2) the

Ê µ ( ) positive (2) (+) 3 1

⌫ are the scalar,

Ê ⌫

(+) 3and negative ( ˆF

|E +1 | 2 +|E

F (2F 1)


( 2 µ ˆF⌫ ˆF frequency

angular vector momentum + ˆF


is the ellipticity


F (2F 1) 2 µ ˆF⌫ + ˆF

and ˆFµ momentum ) tensor

components operator, ˆF

i of the electric field. For an


with w(fw) of strongly ↵ w (bw) guided by| 2 counter-propagating regime: (for E 4 (fw,bw) single 2 i , beam) where w (fw,bw) are the



⌫ ˆFµ ) ˆF

3 µ⌫ atomic i operator, , withdynamic Î and withĴ polarizabilities,

Îthe and nuclear Ĵ the nuclear


and electronic and electronic angular angular momentum momentum operators, operators, µ, ⌫ 2 of the electric field,

Ê 32 { µ, µ⌫ 1, ⌫ 0, 2 ,

= Î (+) and ˆd the elliptically



Hamiltonianpolarized Ê

+ Ĵ is 1} { are 1, 0, components 1} are components in the in the

µ,⌫the (

atomic ) electric



an atom beam,


interacting the vector

and Ê

with shift


ancan the

electric be as


field large as scalar shift, and can,

radial frequencies for the forward A simple and backward schematic propagating for vector-shift beams. cancellation Generally, field the with operator. two-photon detuning Taking⇤ fb

le approximation: for example, are the positive be used and to cancel negative the frequency di↵erential 157 components light shifts of Rubidium the electricatoms field, confined

total angular

spherical spherical tensor basis, tensorand basis, Ĥ0,

momentum counter-propagating

and Ĥ Ĥ0,

operator, with beams.

into Î and Ĵ the nuclear

nd (0) between account

, electronic

ˆF ↵ (1) = and Î + ↵ Ĵ

angular (2) in forward the

isare athe 3Datomic and

the momentum optical backward hyperfine

scalar, total vector lattice beams


angular and [43]. structure, can be set |⇤| this Hamiltonian |⇤

1 ,andĤ2 tensor Ĥmomentum µ, 1 ,andĤ2 ⌫atomic are

2 {


1, dynamic are


terms operator,


the fb | max(w


associated polarizabilities,



withassociated Î trap can , ⇥ and gs be), thereby decomposed removing


the Ĵ


the with scalar, nuclear the scalar,


pherical d↵ (1) Ê and spurious (

vector, ) its

are tensor



↵ (2) the two-photon vector, and are positive basis,

the tensor The angular and


scalar, Ĥprocesses and and ls light last tensor


vector shifts, light and respectively. shifts, tensor respectively. atomic The dynamic light The shifts light polarizabilities,

U scalar shifts , U vector scalar ,andU , U vector tensor ,andU tensor

( ) are arising the positive arising from each from and term each negative Ĥ0, = negative momentum term (e.g., ˆd ·





frequency ,andĤ2 are components the terms

µ, ⌫ 2





of the 1, 0,


electric 1}


are field, the





Ĥ2 Ê, two-photon in Eq. (2) Stark represents shift) as well the as tensor parametric (1) shift. heating It vanishes due to the forintensity

the atoms with


[40, have termbeen frequency have expressed beencomponents expressed explicitly explicitly in Refs. electric in [40, Refs. 41].

ector, Ĵ spherical is


and the


atomic tensor tensor total

light total angular basis, shifts, angular and momentum

respectively. momentum Ĥ0, Ĥ 1

F =1/2 ,andĤ2 The operator, [41]. +

modulations (see footnote b). Specifically, for w (fw,bw) light are = shifts wwith the a

InthecaseoftheD +(⇤ Îterms U± and ⇤ fb field, [40, 41].

scalar ,/2) Ĵassociated U with


nuclear ,andU (1) 2 with transition 1 the h scalar, of Cs, that we


e electric tensor

is the atomic For dipole two-level operator

total For angular two-level atoms and

momentum with Ê is

atoms ground the electric

withoperator, ground and excited field

and with states operator.

excited Î and |gi, states Ĵ|ei, Taking

fb /2

, we achieve

the the |gi, nuclear scalar |ei, the shift scalar U

rising ctronic vector, from angular each andconsider momentum tensor here,

term have light been operators, it shifts, will depend

expressed respectively. µ, ⌫explicitly 2 only { 1, onThe 0, the

in1} Refs. light electronic are components [40, shiftsangular 41]. U scalar in, momentum Uthe

vector ,andU scalar

Ĵshift for tensor Udetunings




atomic shift

al nictensor angular can be approximated hyperfine Ĥ

can momentum be ls

approximated operators, by U by µ, U scalar ⌫ /{

|E| 1, 2 scalar / |E| 2 / for detunings 0, / 1} forare detunings components = ! ! a = large ! in! compared the a large compared to the

For arising two-level basis, from large cancellation

and each atoms compared Ĥ0, = structure,

term Ĥ0 +

to the

ensor basis, and Ĥ0,

with Ĥ 1 ,andĤ2 have Ĥ1 this +

ground been theĤ2

Hamiltonian can be decomposed

and are 6P expressed excited the terms states explicitly associated |gi, |ei, Refs. with the scalar the [40, scalar, 41].

cal tensor components= parameterized ↵ shift U scalar

an andbe tensor approximated Forlight two-level shifts, by

Ĥ (0) Ê ( ) · Ê 3/2 excited state hyperfine structure, and vanish for J = 1

Figure C.2: A simple schematic

atoms U 1 respectively. ,andĤ2 are (+) for vector-shift cancellation with counter-propagating beams. LinearlyIt

polarized will(x-polarized) therefore Ĥ

[40, 41]. by the dynamic polarizability ↵(!)


the terms associated with the scalar,

scalar / with |E| 2 forward (cancel) ⇤ fb



ground / The

only (backward)

for light


detunings andshifts onpropagating the

excited U

excited field E

= scalar ! states , ! U 4 (fw)



a large |gi, ,andU

of the Cs D

|ei, compared the tensor scalar 2 transition, inducing

i ( E 4 (bw)

i ) induces a vector shift V vector

( V vector ) on the Zeeman to shift U scalar

(1) (Ê(

from tensor can each be light term approximated shifts, have respectively. been +i↵ ) sublevels

⇥Ê on the

by expressed


U scalar

The (+) for atoms along

⇤ 2


F + O(1/⇤3 )


ˆx-direction, due the ellipticity

m )·ˆF

/ explicitly |E| F 0

light sublevels 2 / shifts for in Refs.


detunings U scalar [40, , U41].



= !,andU m (2)


! 2 ˜z+

(˜z ) on the x-z

plane. By combining the forward and backward fields, we can cancel the inhomogeneous

a large tensor compared to the

r two-level each termatoms have with been+ ground expressed P F .


0 Zeeman broaden-

of⇤V O(1/⇤ vector from 2 ). the trapping

to the second ordering

↵ (2) and Ê ( explicitly excited ) states in Refs. |gi, [40, |ei, the 41]. scalar shift U scalar

approximated o-level atoms by with U scalar

ground / µ,⌫|E| and 2 µ Ê ⌫


beams { E 4 red , E 4 blue }. The

3 1

( ˆF


F (2F 1) 2 µ ˆF⌫ + ˆF

between the counter-propagating


⌫ ˆFµ ) ˆF

i bluedetuned

fields { E

Ĥ 2 ls • = Tensor Ĥ0 + Ĥ1 shift: + Ĥ2 = !

4 (fw)

blue , E 4 (bw)


} is averaged over the motional and internal dynamics of the atoms by setting an

3 µ⌫ ,

= ↵ (0) Ê ( ) 2.2. · Ê (+)

offset frequency ⇤

Evanescent fb between the two fields with

/ optical excited for detunings traps states using fb w

|gi, = ! the |ei, ! fundamental trap , ⇤ hfs , where w trap and

the a large scalar compared shift mode hfs are trap frequency

Uto scalar


the waveguide

and the hyperfine spacing (in units of frequency) for the ground state, respectively.



by U scalar / |E| 2 / for detunings = ! ! a large compared to the


where +i↵ ↵ (0) (Ê(

Simulating When

, ↵ ) (1) ⇥Ê (+) )·ˆF the

F and ↵ (2) radius two-color a of an optical fiber is reduced well (2) below the propagating field

are the scalar, vector and tensor atomic dynamic polarizabilities,

Ê (+) + P propagating field E


and↵ (2) Ê ( wavelength

µ () )

are Ê ⌫

(+) 3

, the 4 Anisotropy fiber of the excited trap

(fw) (helicity q (fw) (4r) ⌥ ˜(z) electronic wavefunction

+ ) with a backward propagating E



F (2Fpositive ( ˆF resulting

1) 2 µ and ˆF⌫ + negative ˆF cladding-to-air


⌫ ˆFµ )

3frequency ˆF


2 waveguide 4 (bw) (exhibiting opposite

supports only the “hybrid”

helicity q (bw) (4r) ⌥ ˜(z) ), as illustrated in Fig. C.2. This backward propagating field E

µ⌫ , components 4 (bw) carries the same

of the electric field,

In the µ,⌫ following, fundamental we input show polarization our mode results stateHE as that of 11 of the [7, E 44]. In this strongly guiding regime, a significant fraction

Lacroute*, ˆF = Î + Choi*, Ĵ is Goban* the atomic et al. New total J. Phys. angular (2012); 4 (fw) trap , butcalculation, has a detuning ⇤

momentum arXiv:1110.5372 fb

aslarge further enough elaborated (i.e., ⇤ fb win trap , section ⇤ hfs ), such C.5. First, we

operator, with Î and Ĵ the nuclear

y considering the Hamiltonian for an atom interacting with an electric field

intoA account diameter

state-insensitive, the below atomic the optical hyperfine wavelength.

compensate structure, The potential thisU Hamiltonian trap for such a nano-wire

nanofiber can be trap decomposed is shown in

ipole approximation:

into itsFig. spherical 5 for the tensor case of components atomic Cesium parameterized and a fused silica bynano-wire the dynamic of diameter polarizability d 500 nm. ↵(!) As

demonstrated [35], atoms can be trapped in an array of potential wells parallel to the z -axis of

Light shift [40, Hamiltonian: 41, 42]:

the fiber Ĥand ls spaced = ˆd along · Ê, the + red-detuned surface potentials standing-wave (crossover by between (1) vdW & CP)


2 . Two sets of trapping wells

Tensor decomposition:

extend along the z-axis


s the electric dipole operator ls =

and Ĥ0 +

Ê is Ĥ1



the Ĥ2

by an azimuthal angle of . For the case of linear polarization

parallel the x-axis electric field operator. Taking

= ↵

nt the atomic hyperfine structure, (0) for


this ( )


, · Ê

Hamiltonian (+) Fig. 5(b) displays the potential U


the x z plane, with the

Non-trivial complex set of polarizations trap minima shown of the along can decomposed

(1) (Ê(

herical tensor components parameterized +i↵ ) ⇥Ê

evanescent the axis (+) waves of the fiber.


3D state-insensitive trapping

With modest input by F the dynamic polarizability ↵(!)


+ P powers ~ 40mW, trap depths ~1mK



↵ (2) Ê µ ( ) Ê (+) 3 1

( ˆF F (2F 1) 2 µ ˆF⌫ + ˆF 1

⌫ ˆFµ ) ˆF


• is should not a good be readily quantum achievable. number here!

2 3 µ⌫ ,

• Energy Figure eigenstates 5. An obtained optical


trap by locally U

trap for Cesium atoms around

Ĥ ls = Ĥ0 diagonalizing + Ĥ1 a + nano-fiber, Ĥ2the Hamiltonian which is (adiabatic indicated solution) by the gray shaded

= ↵ (0) where

Ê ( ) ↵ region. · (0) Ê

, (+) ↵ (1) U and trap is ↵ generated (2) are theby scalar, two evanescent vector and fields tensor that atomic dynamic polarizabilities,

• Since

Ê (+) the provide atomic


(1) (Ê(

+i↵ ) ⇥Ê Ê ( (+) )·ˆF

) 3-dimensional wavepacket confinement is so tightly confined, for the trapped atoms

it is possible outside drive the are forbidden 500 thenm positive diameter transitions and optical negative fiber, shown frequency in (a) components


of the electric field,


+ P the x y plane, and in (b) the plane. Specifically, U


ˆF = Î + Ĵ is the atomic h total

↵ (2) Ê µ ( results ) Ê ⌫

(+) from two counter-propagating

3 1

( ˆF


F (2F 1) 2 µ ˆF⌫ + ˆF

red-detuned momentum


⌫ ˆFµ ) ˆF

i operator, with Î and Ĵ the nuclear

and electronic angular momentum operators, 2 beams,

and a blue-detuned beam in a so-

3 µ, µ⌫ ⌫ 2 ,

Radial adiabatic potentials

{ 1, 0, 1} are components in the

µ,⌫ configuration [29], as shown

spherical tensor basis, and Ĥ0,

in the inset. The standing

wave structure of the attractive Ĥred-detuned 1 ,andĤ2fields are and the the terms associated with the scalar,

, ↵ (1) and ↵ (2) repulsive force from the blue-detuned beam enable

vector, are the trapping and scalar, tensor of vector single light and atoms shifts, tensor at each respectively. atomic node of dynamic U The light polarizabilities, shifts U scalar , U vector ,andU tensor

ˆ ( ) trap near the

are the positive arising dielectric from and each negative waveguide termfrequency have despite beenthe components expressed strong attraction explicitly of thefrom

electric in Refs. field, [40, 41].

van der Waals forces from the surface.

is the atomic total For angular two-levelmomentum atoms withoperator, ground and with excited Î andstates Ĵ the|gi, nuclear |ei, the scalar shift U

We achieved trapping times for Cesium atoms of


onic angularcan momentum be approximated = 50ms operators, in a bytwo-color µ, U scalar ⌫ 2 /{

|E| trap 1, 2 0, / with 1} forare detunings wavelengths components = ! in! the a large compared to the

ensor basis, and Ĥ0, red

Ĥ 1064 1 ,andĤ2 nm and are bluethe 780 terms nm. Moreover, associated for with two the scalar,

d tensor light shifts, parallel respectively. chains with The total light atom shifts number U scalar

N=2000, , U vector

the ,andU tensor

m each term have been



observe an


optical depth



= 8, corresponding

[40, 41].


an average absorbance per atom of = 0.65%.Inspired

o-level atoms withby ground this work, andwe excited have investigated states |gi, trap |ei, designs the scalar that shift U scalar

roximated by U scalar mitigate / |E| some 2 / for problems detunings for earlier = implementations ! ! a large compared [35]. to the

Namely, the excited states of the 6P32

manifold are not

Lacroute*, Choi*, Goban* et al. New J. Phys. (2012); arXiv:1110.5372

Two-color magic nano-fiber trap

500 nm

Flame-brushing technique

previous works on hollow-core fibers (Ketterle, Lukin & Vuletic)

& nanofibers (Hakuta, Rauschenbeutel)

Phys. Rev. Lett. in preparation (2011).


Two-color magic nano-fiber trap





Thermal atoms vs. Trapped atoms

• Determination of atom number and

resonant optical depth





-60 -40 -20 0 20 40 60



Trap lifetime measurement

• State-insensitive trap (i.e., cancellation of

fictitious magnetic field due to nontransverse

evanescent fields + use of

magic wavelengths)

Trapped atoms (with cooling)



d 0



pulsed PG




0 50 100 150 200 250 300 350


• limited by laser-induced parametric heating of the motional state

due to spontaneous Brillouin scattering in the fiber

• Degenerate Raman sideband cooling

Phys. Rev. Lett. in preparation (2011).

Cavity QED with Atomic Mirror

Single atom coupling

a) Single atom coupling

E in

Γ 1D

r 1

E in

b) Atomic Bragg mirror

t 1

E in

Chang et al. arXiv:1201.0643 (2012)


c) Cavity QED

d M d I

E scattered E d M

E in

+1 −1 +1 −1 −1 +1 −1 +1

j = 0

d) Quantum information bus

d I

Photon transport

Classical interpretation

d induced

d M • Resonantly driven dipole phased by 90 degrees relative to incident field


Photon in

transport • Re-emitted in 1D field phased by 90 degrees relative to dipole Coupled system



FIG. 1: Illustrations of di↵erent configurations of a coupled at

r NM

E in

j = 1 2 • Perfect N M t NM


E in

of incident and re-emitted fields in forward direction

Photons always scatter back to the waveguide

Transfer matrix

coupling. The atom spontaneously emits into the fiber and fr



photon loss)

and transmission spectrum spectively. In the linear regime, the atom scatters a guided in

FIG. 1: Illustrations of di↵erent configurations of R= a coupled 1 1/ P atom-fiber system. a) Single atom


, the atom blocks the waveguide On resonance, transmission a single amplitudes atom is optically r 1 ,t 1 . b) N M atoms in a chain with la

coupling. and the Thephoton atom spontaneously must be reflected. emits into the fiberT=|t| and 2

free space


at rates

to single

1D and


“Bragg 0 mirror,”


In the linear regime, the atom scatters a guided input fieldIn Econtrast in with reflection to QED” cavity configuration,

with linear reflection and transmission amplit

A near-perfect mirror for single photons Bragg reflection from

and QED, collective strong two atomic atom-

mirror Braggfor mirrors (located at . 1 apple j

transmission amplitudes r 1 ,t 1 . b) N M atoms in a chain with lattice constant photon d M

coupling form anis atomic achieved on a single

Shen and Fan, Opt. Lett. 30, 2001 (2005). Loss pass a cavity, which enhances the coupling of an impurity atom (green

“Bragg mirror,” with linear reflection and transmission amplitudes r NM ,t NM . c) In


the “cavity

the impurity and its nearest neighbors is d I . The relat

• A resonantly driven dipole phased by π/2 relative

QED” configuration, two atomic Bragg mirrors photon

(located eg

at 1 apple j apple N m and N m apple j apple 1) form

to the incident field.

spin wave comprising the cavity excitation are denoted in red. A

• a cavity, Re-emitted which enhances field phased the coupling by π/2 of anrelative impurityto atom the (green, j = 0) to the fiber. drive The distance the impurity atom. d) Quantum information transfer can

between induced the impurity dipole. and its nearest neighbors is d I . The relative phases ±1 of the impurity mirror atom atoms p, q in the “quantum information bus” configurat

• Destructive interference between the incident





comprising the



in the





denoted in red. An external field E can initially be used sittoin separate cavities within a long chain of mirror at

drive the impurity atom. d) Quantum information transfer can occur between two well-separated

mirror atoms between them are flipped into a transparent hyperfi

impurity atoms p, q in the “quantum information bus” configuration. Here the two impurity loads the atoms impurity atoms into a new, common cavity mode defin

d M

a) Single atom coupling

E in

Γ 1D

r 1

E in

b) Atomic Bragg mirror

E in

r NM

E in

j = 1 2

d M



t 1

E in

Collective atom mirror

t NM

E in


c) Cavity QED

d M

−1 +1

d) Quantum inform

d I



d I


What’s next on the horizon

Scalable quantum networks

with hybrid quantum systems

trap for Cesium atoms around

dicated by the gray shaded

y two evanescent fields that

When quantum optics meets quantum spins

ation of single J. R. Petta, optical plasmons in metallic

1 A. C. Johnson, 1 J. M. Taylor, 1 E. A. Laird, 1 A. Yacoby, 2

U M. D. Lukin,

ires coupled to quantum 1 C. M. Marcus, 1 M. P. Hanson,


3 A. C. Gossard 3


in a so-

ρ (µm)

Semiconductor Quantum Dots

Interdot tunneling (at a rate set by voltage

inement for the trapped atoms


) allows electrons to be moved between

er optical fiber, shown in (a)

the plane. Specifically,

dots when the detuning parameter e º V R

opagating red-detuned beams,


is adjusted. Measurements are performed

We demonstrated coherent control of a quantum two-level system based on in a dilution refrigerator with electron temperature

optics T

n in the inset. The standing Quantum optics with neutral atoms

two-electron spin states in a double quantum dot, allowing state preparation,


v 1,4 *, A. Mukherjee 1 *, C. L. Yu 2 *, D. E. Chang 1 , A. S. Zibrov 1,4 , P. R. Hemmer 3 , H. Park 1,2 & M. D. Lukin 1 e

Èwith 135 mK, trapped determined ions from

ive red-detuned fields and the

blue-detuned beam enable coherent manipulation, and projective readout. These techniques are based on Coulomb blockade peak widths. Gates L and

Haroche, Kimble, Grangier, Bloch 1990

each node of U rapid electrical control of the exchange interaction. Separating and later Wineland, R are connected Blatt, via low-temperature Monroe bias tees

trap near the

te the strong attraction from recombining a singlet spin state provided a measurement of the spin to high-bandwidth coaxial lines, allowing

he surface.

dephasing time, T 2

*, of È10 nanoseconds, limited by hyperfine interactions rapid (È1 ns) pulsing of these gates (15).

g etimes interaction for Cesium between atoms single of photons with the andgallium individual arsenidenanowire, host nuclei. causing Rabi the oscillations wire’s ends of to two-electron light up. Non-classical spin photon High-frequency manipulation of a single elec-

thedemonstrating the gigahertz bandwidth of

or rs istrap an outstanding with wavelengths problemstates in quantum were demonstrated, science correlations and spin-echo between pulsethe sequences emissionwere fromused the to quantum suppress

control hyperfine-induced over light dephasing. ends of the Using nanowire these quantum demonstrate control that techniques, the latter astems fromthis thesetup, was reported in (16).

dot andtron,

ng. 80 nm. It is Moreover, of interestfor for two ultimate


ell as


for potential



the coherence such as time efficient for two-electron generation spin of states single, exceeding quantized1 plasmons. microsecond Results was from a large Quantum point contact (QPC) sensors

ion 2 , single-photon switching 3 observed. and transistors 4 , and number of devices show that efficient coupling is accompanied fabricated next to each dot serve as local electrometers

(17, 18), showing a few-percent

epth = 8, corresponding to

tical coupling of quantum bits 5,6 . Recently, subces

have been made towards Quantum these coherence goals, based and entanglement on eous emission, have and in good demonstrate agreement coherent with theoretical control of predictions. this reduction of conductance when a single charge

by more than 2.5-fold enhancement of the quantum dot spontan-

atom of = 0.65%.Inspired

estigated trap designs that

oton fields around an emerged emitter using as physical high-finesse bases for informationprocessing

a cavity-free, schemes broadband that use two-state excitations quantumof charge-density of the exchange waves interaction. and their Weassociated first showelectromag-

by the conductance, g s

Surface plasmons, systemorthrough surfacethe plasmon use of fast polaritons, electricalare control propagating is added to the adjacent dot. Figure 1B shows

2,3,5–8 arlier implementations [35].

. Here we demonstrate , of the right QPC sensor as

f the 6P32

engineering manifold are not

photon–emitter systems interactions (quantum 4,9 bits viaor subnfinement

qubits) netic to provide fields on the direct surface time-domain of a conductor measurements 10 . Muchthat likethe

optical a function of V L

and V R

near the two-electron

of optical fields efficient near computation metallicand nano- secure modes communica-

of a conventional time-ensemble-averaged dielectric fibre, dephasing a broad continuum time (T 2

*) ofregime. surface

Each charge state gives a distinct value

plasmon of en-

modes of thiscan qubit be is confined È10 ns, on limited a cylindrical by hyperfine metallicof wire g s

When a single CdSe tion quantum (1, 2). dot Although is optically quantum control ,decreasingeachtimeanelectronisadded

e proximity to a silver 8 nanowire, tanglement emission has beenfrom realized thein isolated and guided atomicalong interactions. the wire axis We

couples directly Quantum to guided optics surface with plasmons SPP

then (Fig. demonstrate 1a). However, Rabi oscillations


14,31 in the , the two-spin

as opposed to the to system or when an electron is transferred

systems, its extension toinsolid-state the dielectric systems—

Scalable waveguides quantum thin wires space can(including maintain networks

a 180-ps propagation fromof

the left dot to the right dot. Labels (m,n)

motivated by the prospect of scalable device SWAP operation between two electron in each region indicate the absolute number of

a Park, fabrication—remains Lukin a demandingb


goal (3, 4), particularly because of the showing an extended spin coherence time, T

with spins) hybrid and implement quantum spin-echo sequences, systems electrons confined on the (left, right) dot in the

50 nm wire


, ground state. We focus on transitions involving

stronger coupling of solid-state qubits to their beyond 1 ms.


(0,2) and (1,1) two-electron states, where previous

experiments have demonstrated spin-


100 nm wire

radenvironment. Understanding this coupling and Isolating and measuring two electrons.

learning how to control quantum systems 10 in Gate-defined double quantum dot devices are selective tunneling (12, 13, 19, 20).

the solid state is a major challenge of modern fabricated using a GaAs/AlGaAs heterostructure

Quantum grown by molecular optics beam with epitaxy electrons with a ative energy detuning e of the (0,2) and (1,1)

Voltage-controlled exchange. The rel-

condensed-matter physics (5, 6).


An attractive candidateΓ pl

for a solid-state two-dimensional electron gas 100 nm below charge states can be rapidly controlled by


qubit is based on semiconductor quantum dots, Petta, Gossard


which allow controlled coupling of one or

more electrons, using rapidly switchable voltages

applied to electrostatic gates (7–9). 0 Recent

experiments suggest that spin in quantum


20 40 60 80

Distance from wire (nm)

dots may be a particularly promising holder of


quantum information, because the spin relaxation

time (T 1


) can approach tens of milliseconds

Max. d

(10–13). Although gallium arsenide

(GaAs) is a demonstrated exceptional material


Quantum cryptography for fabricating with quantum quantum dots, it has dots the potential

0.2 drawback that confined electrons in-


teract withEdamatsu

on the order of 10 6 spin-3/2 nuclei


through the hyperfine interaction. Here we

present a quantum two-level system (logicalθ

Silicon quantum computing

qubit) based on two-electron spin states (14) Fig. 1. (A) Scanning electron micrograph of a sample identical to the one measured, consisting of

0 1 2


0 20 40 60 80 100 120

Kane, Itoh, Morton

electrostatic gates on the surface of a two-dimensional electron gas. Voltages on gates L and R

z (µm)

θ (degrees)

Enhancement factor, P

Scattered intensity (a.u.)

Efficiency, η

each dot to adjacent reservoirs, allowing

electrons to be transferred into the dots.

Downloaded from on August 4, 2011

Quantum optics with electron spin ensembles

Awschalom, Schoelkopf

Quantum computing with defects

Lukin, Awschalom

Myriads of routes towards quantum networks

In all cases, spin control for QIS

Schellingstrasse 4, 80799 München, Germany

Outlook – Exciting New Scientific Frontiers

Scientific opportunities enabled by hybrid quantum networks

• long-lived quantum memory and robust quantum interface

quantum metrology (e.g., optical lattice clocks)

quantum simulator for quantum spin models

• spin frustration and entanglement (e.g., Pauli’s spin ice)

• high T c superconductivity and W-states

• entanglement in biological quantum DOI: 10.1103/PhysRevLett.99.140403


• entanglement in quantum critical phenomena

“Entanglement” transition

Choi et al. Nature 468, 412 (2010)

Optical control of electronic and nuclear spins

Togan et al. Nature 466, 730 (2010)

1 Max-Planck-Institut für Quantenoptik and Fakultät für Physik der Ludwig-Maximilians-Universität,

2 Laboratoire Kastler Brossel de l’E.N.S., 24 Rue Lhomond, 75231 Paris Cedex 05, France

(Received 22 March 2007; published 3 October 2007)

We theoretically study the coupling of Bose-Einstein condensed atoms to the mechanical oscillations of

a nanoscale cantilever with a magnetic tip. This is an experimentally viable hybrid quantum system which

allows one to explore the interface of quantum optics and condensed matter physics. We propose an

experiment where easily detectable atomic spin flips are induced by the cantilever motion. This can be

used to probe thermal oscillations of the cantilever with the atoms. At low cantilever temperatures, as

realized in recent experiments, the backaction of the atoms onto the cantilever is significant and the system

represents a mechanical analog of cavity quantum electrodynamics. With high but realistic cantilever

quality factors, the strong coupling regime can be reached, either with single atoms or collectively with

Bose-Einstein condensates. We discuss an implementation on an atom chip.

Quantum optics and condensed matter physics show a

strong convergence. On the one hand, quantum optical

systems, most notably neutral atoms in optical lattices,

have been used to experimentally investigate concepts of

condensed matter physics such as Bloch oscillations and

Fermi surfaces [1]. On the other hand, micro- and nanostructured

condensed matter systems enter a regime described

by concepts of quantum optics, as exemplified by

circuit cavity quantum electrodynamics [2], laser-cooling

of mechanical resonators [3], and measurement backaction

effects in cryogenic mechanical resonators [4]. A new

exciting possibility beyond this successful conceptual interaction

is to physically couple a quantum optical system

to a condensed matter system. Such a hybrid quantum

system can be used to study fundamental questions of

decoherence at the transition between quantum and classical

physics, and it has possible applications in precision

measurement [5] and quantum information processing [6].

Atom chips [7] are ideally suited for the implementation

of hybrid quantum systems. Neutral atoms can be positioned

with nanometer precision [8] and trapped at distances

below 1 m from the chip surface [9]. Coherent

control of internal [10] and motional [11] states of atoms in

chip traps is a reality. Atom-surface interactions are sufficiently

understood [7] so that undesired effects can be

mitigated by choice of materials and fabrication techniques.

This is an advantage over systems such as ions or

polar molecules on a chip, which have recently been

: hyperfine spins

Quantum optomechanical coupling

considered in this context [6,12]. A first milestone is to

realize a controlled interaction between atoms and a nano-

• Ubiquitous coupling between

heterogeneous quantum systems:


• g ls : Coupling between light and sound

PACS numbers: 03.75.Nt, 39.90.+d, 42.50.Pq, 85.85.+j

• g lm : Coupling between zipper&cavity&fabricat

light and matter

• perature. Strong At lower coupling resonator criteria: temperatures, g ls =g the lm

backaction >γ,κ

of the atoms onto !'Stoichiometric'Si the resonator is significant 3 N 4 'is'used'to'form'th and the

coupled system realizes for'two'reasons:'(i)'mechanical'properJ

a analog of cavity

quantum electrodynamics nitride'have'recently'been'shown'to'be

(CQED) in the strong coupling

regime. We specify and'(ii)''opJcal'power'handling'capabil

in detail a realistic setup for the experiment,

which can


be performed with available atom

chip technology and thus allows one to explore this fascinating

field already ! today. Electron'beam'lithography'and'direct'p

The physical situation (ICPKRIE)'of'nitride'are'used'to'define'th

is illustrated in Fig. 1(a). 87 Rb

atoms are trapped inpaLerning'

a magnetic microtrap at a distance y 0

above a cantilever ! resonator, Resist'strip,'followed'by'KOH'silicon'we

which nanofabricated on

the atom chip surface.


The cantilever tip carries a singledomain

Optomechanical ferromagnet whichcrystal creates a(Painter, magnetic field 2010) with a

strong gradient G! m . Slot'gaps'of'

Harnessing macroscopic matter-light quantum coherence

Nano integrated device

Coherent control of quantum


Quantum information science

Stimulated coherence and quantum control

Inventions of quantum devices

from “Q. transistors”,

“Q. wires”, “Q. harddrives,” to

“Quantum interfaces”



Lithographically patterned

quantum networks

Strongly correlated systems

Investigation of quantum entanglement naturally

occurring in the mesoscope

(i.e. quantum spin models) ...

Multipartite entangled spin waves

Nonlocal phases induced by coherent and mediated

interactions of quantum nodes via entanglement

distribution over scalable quantum network

Thank you !

Caltech quantum optics

Atomic ensemble lab

Kyung Soo Choi, former CPI PD (now at KIST)

Akihisa Goban, G3 Martin Pototschnig, PD

Ding Ding, G1

Lucile Veissier, LKB Paris

Scott Papp, NIST Boulder

Julien Laurat, LKB Paris

Hui Deng, University of Michigan

Chin-Wen Chou, NIST Boulder

Daniel Felinto, Recife

current members

recent alumni since 2006

Hugues de Riedmatten, ICFO Barcelona

Microtoroid lab

Daniel Alton, Pol Forn-Diaz, Clement

Lacroute, Nate Stern

Optomechanics lab

Darrick Chang, Jonathan Hood, Kang-

Kuen Ni, Yi Zhao, Dalziel Wilson

Principal Investigator

Prof. H. Jeff Kimble

Theoretical collaboration

University of Oregon

Pavel Lougovski, Stanford

Prof. Steven van Enk

IQIM, Caltech

Alexey Gorshkov

Liang Jiang

Darrick Chang (ICFO)

Funding sponsors: NSF/North. Grumm./DoD/AFOSR MURI/IQIM/KIST institutional program

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