Index OMC_final - Harvard University

Table of Contents
WORKSHOP SCHEDULE ............................................................................................................ 3
PARTICIPANTS ............................................................................................................................. 5
MAPS/TAXI .....................................................................................................................................27
ABSTRACTS IN ALPHABETICAL ORDER BY AUTHOR
Quantum-Optomechanics in the Weak and Strong Coupling Regime
Markus Aspelmeyer....................................................................................................8
Towards Quantum Superpositions of a Mirror
Dirk Bouwmeester ......................................................................................................9
From Cavity Optomechanics to the Dicke Quantum Phase Transition
Ferdinand Brennecke..................................................................................................10
Linear and Quadratic Optomechanics with an Array of Ultracold
Atomic Ensembles
Daniel Brooks...............................................................................................................11
Ultracold Atoms Coupled to a Micromechanical Membrane
David Hunger...............................................................................................................12
Optomechanics of a Quantum-Degenerate Fermi Gas
Rina Kanamoto ............................................................................................................13
Dynamics of Optomechanical Arrays
Florian Marquardt .......................................................................................................14
Nonlinear Optomechanics: Quadratic Coupling and the
Single-Photon Regime
Andreas Nunnenkamp ...............................................................................................15
Radiation Pressure at the Nanoscale: Classical- and Quantum- Optical
Applications
Oskar Painter................................................................................................................16
The Photon Blockade Effect in Optomechanical Systems
Peter Rabl......................................................................................................................17

Table of Contents
Optical Trapping and Cooling of Glass Microspheres
Mark Raizen .................................................................................................................18
Optomechanical Matter-Wave Interferometer for Microspheres
Oriol Romero-Isart ......................................................................................................19
Optomechanics with a Silicon Nitride Membrane Approaching the
Quantum Regime
Jack Sankey...................................................................................................................20
Cavity Optomechanics: Beyond the Ground State
Swati Singh...................................................................................................................21
Optomechanical Cooling and Amplification in a Chip-Scale
Integrated Circuit
Hong Tang ....................................................................................................................22
Circuit Cavity Electromechanics in the Strong Coupling Regime
John Teufel ...................................................................................................................23
A Phonon-Tunneling Approach to Clamping Losses of
Mechanical Resonators
Ignacio Wilson-Rae .....................................................................................................24
Radiation Pressure and Quantum Noise
Christopher Wipf ........................................................................................................25
Hybrid Systems: Atoms and Opto-Nanomechanics
Peter Zoller ..................................................................................................................26

Schedule
MONDAY, FEBRUARY 7 Phillips Auditorium, ITAMP, 60 Garden St., Cambridge
8:00 Morning Coffee & Pastry, Registration
8:30 Introduction
Session I Big Ideas I
Chair: Pierre Meystre
9:00 Peter Zoller | Hybrid Systems: Atoms and Opto-Nanomechanics
9:40 Marcus Aspelmeyer | Quantum-Optomechanics in the Weak and Strong
Coupling Regime
10:20 Morning Break
11:00 Mark Raizen | Optical Trapping and Cooling of Glass Microspheres
11:40 Oriol Romero-Isart | Optomechanical Matter-Wave Interferometer for
Microspheres
12:20 Lunch
Session II Big Ideas II
Chair: Dan Stamper-Kurn
2:00 Eric Adelberger | Low-Frequency Torsion Oscillators in Gravitational Physics
2:40 Christopher Wipf | Radiation Pressure and Quantum Noise
3:20 Dirk Bouwmeester | Towards Quantum Superpositions of a Mirror
4:00 Break
4:40 Panel Discussion: Konrad Lehnert, Ignacio Cirac, Mark Raizen, Oskar Painter
Moderator: Nergis Mavalvala
5:45-7 Reception: Perkin Lobby
TUESDAY, FEBRUARY 8 Phillips Auditorium
Session III State of the Art
Chair: Konrad Lehnert
9:00 Ferdinand Brennecke | From Cavity Optomechanics to the Dicke Quantum
Phase Transition
9:40 Dan Brooks | Linear and Quadratic Optomechanics with an Array of Ultracold
Atomic Ensembles
10:20 Break
11:00 Rina Kanamoto | Optomechanics of a Quantum-Degenerate Fermi Gas
11:40 Ignacio Wilson-Rae | A Phonon-Tunneling Approach to Clamping Losses of
Mechanical Resonators
3

Schedule
12:20 Jack Sankey | Optomechanics with a Silicon Nitride Membrane Approaching
the Quantum Regime
1:00 Lunch
Session IV State of the Art II
Chair: Mark Raizen
2:40 Tobias Kippenberg
3:20 Florian Marquardt | Dynamics of Optomechanical Arrays
4:00 John Teufel | Circuit Cavity Electromechanics in the Strong Coupling Regime
WEDNESDAY, FEBRUARY 9 Phillips Auditorium
8:30 Morning Coffee & Pastry
Session V Hybrid Methods
Chair: Oskar Painter
9:00 Mukund Vengalattore|
9:40 Swati Singh | Cavity Optomechanics: Beyond the Ground State
10:20 Coffee
11:00 Andreas Nunnenkamp | Nonlinear Optomechanics: Quadratic Coupling and
the Single-Photon Regime
11:40 Hong Tang | Optomechanical Cooling and Amplification in a Chip-Scale
Integrated Circuit
12:20 Lunch
Session VI Hybrid Methods (cont’d)
Chair: Juan Ignacio Cirac
2:00 David Hunger | Ultracold Atoms Coupled to a Micromechanical Membrane
2:40 Peter Rabl | The Photon Blockade Effect in Optomechanical Systems
3:20 Thank You and Closing Thoughts
Walk to Physics: Physics, Harvard University, Physics Colloquium Room: Jefferson 356
4:00 Coffee in Jefferson 356
4:30 JAPC Talk| Oskar Painter: Radiation Pressure at the Nanoscale: Classical- and
Quantum-Optical Applications
4

JAMIL ABO-SHAEER
PARTICIPANTS
Darpa, Jamil.Abo-Shaeer@Darpa.Mil
ERIC ADELBERGER
University Of Washington, Eric@Npl.Washington.Edu
MARKUS ASPELMEYER
NIR BAR-GILL
University of Vienna, aspelmeyer-office@univie.ac.at
Harvard University, Nbar-Gill@Cfa.Harvard.Edu
STEVEN BENNETT
Harvard University, bennett@physics.harvard.edu
TIMOTHY BODIYA
KJETIL BORKJE
Massachusetts Institute of Technology, Bodtim@Mit.Edu
Yale University, Kjetil.Borkje@Yale.Edu
DIRK BOUWMEESTER
UC Santa Barbara, bouwmeester@physics.ucsb.edu
NATHAN BRAHMS
UC Berkeley, Tatumd@Berkeley.Edu
FERDINAND BRENNECKE
DANIEL BROOKS
Eth Zurich, Brennecke@Phys.Ethz.Ch
UC Berkeley, tatumd@berkeley.edu
ARAVIND CHIRUVELLI
U niversity Of Arizona, Achiruvelli@Email.Arizona.Edu
A. EGON CHOLAKIAN
Harvard University, aecholakian@post.harvard.edu
JUAN IGNACIO CIRAC
Max-Planck Institute of Quantum Optics, Ignacio.cirac@mpq.mpg.de
PETER HERSKIND
Massachusetts Institute of Technology, herskind@mit.edu
DAVID HUTCHISON
Cornell University David.N.Hutch@Gmail.Com
5

DAVID HUNGER
PARTICIPANTS
LMU Munich, david.hunger@physik.lmu.edu
RINA KANAMOTO
Ochanomizu University, kanamoto.rina@ocha.ac.jp
UTKU KEMIKTARAK
JOHN LAWALL
NIST/JQI, kemiktau@umd.eu
NIST, john.lawall@nist.gov
KONRAD LEHNERT
JILA, konrad.lehnert@jila.colorado.edu
NERGIS MAVALVALA
Massachusetts Institute of Technology, Nergis@Ligo.Mit.Edu
FLORIAN MARQUARDT
University Of Erlangen, florian.marquardt@physik.uni-erlangen.de
PIERRE MEYSTRE
University ofArizona, Pierre@optics.arizona.edu
ANDREAS NUNNENKAMP
ERIC OELKER
OSKAR PAINTER
Yale University, andreas.nunnenkamp@yale.edu
Massachusetts Institute of Technology, Ericoelker@Gmail.Com
Caltech, opainter@caltech.edu
GREGORY PHELPS
PETER RABL
MARK RAIZEN
University of Arizona, gphysics@email.arizona.edu
Austrian Academy of Sciences, peter.rabl@uibk.ac.at
University of Texas at Austin, raizen@physics.utexas.edu
ORIOL ROMERO-ISART
JACK SANKEY
Max Planck Institute for Quantum Optics,
oriol.romero-isart@mpq.mpg.de
Yale Physics, jack.sankey@yale.edu
6

MONIKA SCHLEIER-SMITH
SWATI SINGH
PARTICIPANTS
Massachusetts Institute of Technology, schleier@mit.edu
University of Arizona, swati@physics.arizona.edu
DAN STAMPER-KURN
UC Berkeley, dmsk@berkeley.edu
STEVEN STEINKE
HONG TANG
JOHN TEUFEL
EMRE TOGAN
University of Arizona, Steinke@email.arizona.edu
Yale University, hong.tang@yale.edu
NIST – Boulder, john.teufel@nist.gov
Harvard University, emretogan@gmail.com
MUKUND VENGALATTORE
AMAR VUTHA
Cornell University, mukundv@cornell.edu
Yale University, amar@cua.harvard.edu
RENYUAN WANG
Dsb25@Cornell.Edu
IGNACIO WILSON-RAE
Technical University Munich, Ignacio.wilson-rae@ph.tum.de
CHRISTOPHER WIPF
Massachusetts Institute of Technology Ligo, wipf@ligo.mit.edu
BERNHARD WUNSCH
HAO ZHANG
PETER ZOLLER
Bwunsch@Physics.Harvard.Edu
Massachusetts Institute of Technology, htzhang@mit.edu
Institute for Theoretical Physics, peter.zoller@uibk.ac.at
7

QUANTUM-OPTOMECHANICS IN THE WEAK AND
STRONG COUPLING REGIME
Markus Aspelmeyer
Unversity of Vienna
I will discuss some of our current experiments to achieve quantum optical control over
mechanical quantum states. This includes optomechanics using ultracold cryogenic cavities and
the demonstration of optomechanical parametric downconversion, which is at the heart of
optomechanical quantum entanglement..
8

TOWARDS QUANTUM SUPERPOSITIONS OF A MIRROR
Dirk Bouwmeester
Department of Physics, University of California, Santa Barbara,
& Huygens Laboratory, University of Leiden, the Netherlands
Using a tiny mirror attached to a micromechanical resonator as one of the mirrors in an
interferometer we aim to investigate macroscopic quantum superpositions. We analyze the effects
of finite temperature on the proposed experiment and conclude that an unambiguous
demonstration of a quantum superposition requires the mechanical resonator to be in or near the
ground state. This can in principle be achieved by optical cooling of the fundamental mode,
which also provides a method for measuring the mean phonon number in that mode. We also
calculate the rate of environmentally induced decoherence and estimate the timescale for
gravitational collapse mechanisms as proposed by Penrose and Diosi. We will show experimental
data on optical cooling of an optical trampoline resonator starting from dilution refrigeration
temperatures. Finally we discuss the technical challenges to be overcome in order to test quantum
mechanics in the regime where gravitational effects might interfere.
9

FROM CAVITY OPTOMECHANICS TO THE DICKE QUANTUM
PHASE TRANSITION
Ferdinand Brennecke
Department of Physics, ETH Zürich, Switzerland
Coupling the collective motion of ultracold gases to high-Q optical resonators provides an
approach towards unexplored regimes in cavity optomechanics [1, 2]. In these mesoscopic
systems, the ground state of the mechanical oscillator is naturally prepared by the initial cooling of
the atomic gas. In our experiment, a Bose-Einstein condensate of about 10 5 alkali atoms is
coupled dispersively to the single-mode field of an ultrahigh-finesse optical cavity. A collective
density oscillation of the condensate serves as a mechanical element which couples to the cavity
field intensity. We observe optical bistability already below the single-photon level and a strong
backaction dynamics, in quantitative agreement with a cavity optomechanical model. The
experiment reaches the strong coupling regime of cavity optomechanics, where already single
mechanical excitations have a significant effect on the cavity field.
In a different setting of the experiment exploiting the mechanical effects of light on quantum
gases, we recently observed a non-equilibrium version of the Dicke quantum phase transition [3, 4,
5]. A far-detuned pump field aligned perpendicular to the cavity axis induces a dipole-like
interaction between the cavity field and a collective density wave. Above a critical pump strength
the atoms self-organize on a checkerboard structure, which is associated with a spontaneously
broken symmetry. The cavity decay channel allows us to extract valuable in-situ information about
the system like its phase diagram, the appearance of spontaneous symmetry breaking, and the
vanishing excitation gap close to the critical point. Our observations are quantitatively described
by the Dicke model.
References:
[1] K. W. Murch, K.L. Moore, S. Gupta, D. M. Stamper-Kurn, Nature Physics 4, 561 (2008)
[2] F. Brennecke, S. Ritter, T. Donner, T. Esslinger, Science 322, 235 (2008) [
[3] K. Baumann, C. Guerlin, F. Brennecke, T. Esslinger, Nature 464, 1301 (2010)
[4] R. H. Dicke, Phys.Rev 93(1), 99 (1954)
[5] K. Hepp, E.H. Lieb, Annals of Physics 76(2), 360 (1973)
10

LINEAR AND QUADRATIC OPTOMECHANICS WITH AN ARRAY OF
ULTRACOLD ATOMIC ENSEMBLES
Daniel Brooks
UC Berkeley
Atomic ensembles have a number of advantages as optomechanical oscillators . They can be
cooled to their motional ground state using atomic cooling techniques, have very low thermal
coupling to the surrounding environment, and can be probed in the single-photon strong coupling
regime. We present an experiment using an integrated atom-chip/cavity device operated with
atoms initialized in their motional ground state. Strong magnetic-field gradients from the atom
chip allow us to prepare atomic ensembles centered on locations that are primarily either linearly
or quadratically coupled to the cavity field. In addition, we can alter the light-atom coupling
strength of neighboring atomic ensembles in a 1D array by using a magnetic resonance technique
to address the atomic spin. We also present ongoing studies of the linear optomechanical gain of
the atom-cavity device driven by near shot-noise fluctuations of the light.
11

ULTRACOLD ATOMS COUPLED TO A MICROMECHANICAL MEMBRANE
David Hunger, 1,2 Stephan Camerer, 1,2 Maria Korppi, 1,2,3
Andreas J ̈ockel, 1,2,3 Theodor W. H ̈ansch, 1,2 and Philipp Treutlein 1,2,3
1Max-Planck-Institute of Quantum Optics, Garching, Germany
2Faculty of Physics, Ludwig-Maximilians-University Munich, Germany
3Department of Physics, University of Basel, Switzerland
E-mail: philipp.treutlein@unibas.ch
We report the observation of bi-directional coupling between a mechanical oscillator and the
center-of-mass motion of ultracold atoms. Our experiment realizes a recently proposed system [1]
in which an optical lattice mediates a long-distance coupling between laser-cooled atoms and a
micromechanical membrane. We detect both the effect of the vibrating membrane onto the
atoms as well as the effect of the atoms onto the membrane and find reasonable agreement with a
simple theoretical model. Coupling ultracold atoms to mechanical oscillators opens the exciting
perspective of using the tools of atomic physics to read out, cool, and coherently manipulate the
oscillators’ state [2, 3, 4].
Figure 1: Schematic of our setup: A laser field impinging from the right is partially reflected off a dielectric
membrane and forms a standing wave optical potential for an atomic ensemble. Vibrations of the
membrane’s fundamental mode will shift the standing wave field, shaking atoms in the optical lattice.
Conversely, oscillations of the atomic cloud (center of mass motion) will change the intensity of left/right
propagating field components, thus shaking the membrane via changing the radiation pressure on it.
References:
[1] K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, and T. W. H ̈ansch, Phys.
Rev. A 82 021803 (R) (2010).
[2] D. Hunger, S. Camerer, T. W. H ̈ansch, D. K ̈onig, J. P. Kotthaus, J. Reichel, and P. Treutlein, Phys. Rev. Lett.
104, 143002 (2010).
[3] P. Treutlein, D. Hunger, S. Camerer, J. Reichel, T. W. H ̈ansch, and P. Treutlein, Phys. Rev. Lett. 99, 140403
(2007).
[4] K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble,
Phys. Rev. Lett. 103, 063005 (2009). [4] V. M. Acosta, E. Bauch, A. Jarmola, L. J. Zipp,
M. P. Ledbetter, and D. Budker, Broadband magnetometry by infrared-absorption detection of diamond NV centers
[5] M.P. Ledbetter, C.W. Crawford, A. Pines, D.E. Wemmer, S. Knappe, J. Kitching, and D. Budker, Optical
detection of NMR J-spectra at zero magnetic field, Journal of Magnetic Resonance 199 (2009) 25 29
[6] L.-S. Bouchard, V. M. Acosta, E. Bauch, and D. Budker, Detection of the Meissner Effect with a Diamond
Magnetometer
12

OPTOMECHANICS OF A QUANTUM DEGENERATE FERMI GAS
Rina Kanamoto
Division of Advanced Sciences, Ochanomizu University
We provide a “bottom up” approach to cavity optomechanics [1,2,3] by exploring the interaction
between a light field and a mechanical mode of a quantum-degenerate Fermi gas inside a Fabry-
Pérot cavity [3]. Analogous to the momentum side-mode excitations of a bosonic condensate [2],
the low-lying phonon modes of the fermions are collective density oscillations associated with
particle-hole excitations. The mechanical modes of the fermions hence behave as moving mirrors.
We derive an effective Hamiltonian and propose the observation of optical bistability as an
experimental signature of the optomechanical coupling.
Momentum side modes of cold atoms
References:
[1] K.W. Murch, K.L. Moore, S. Gupta, and D.M. Stamper-Kurn, Nature Physics 4, 561 (2008)
[2] F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, Science 322, 235 (2008)
[3] R. Kanamoto and P. Meystre, Physical Review Letters 104, 063601 (2010)
13

DYNAMICS OF OPTOMECHANICAL ARRAYS
Florian Marquardt
Departments of Physics and Applied Physics, Yale University
In this talk I will address novel features that may be observed in multi-mode optomechanical
systems. I will describe the impact of multi-mode dynamics on phonon lasing (self-induced
optomechanical oscillations). There, Landau-Zener Stueckelberg dynamics of the light field
drastically changes the nonlinear dynamics. I will also describe synchronisation of
optomechanical self-oscillations in an array of coupled oscillators.
14

NONLINEAR OPTOMECHANICS: QUADRATIC COUPLING AND THE
SINGLE-PHOTON REGIME
Andreas Nunnenkamp
Departments of Physics and Applied Physics, Yale University
In optomechanical systems optical and mechanical degrees of freedom are coupled via radiation
pressure, optical gradient, or photothermal forces. To date, the theoretical literature has focused
on systems where the position of the mechanical oscillator is coupled parametrically to the cavity.
In this case, the equations can often be linearized and thus solved exactly.
Motivated by experiments with the membrane-in-the-middle geometry, I will explore the physics
of optomechanical systems in which an optical cavity mode is coupled parametrically to the square
of the position of a mechanical oscillator. In particular, I will derive an effective master equation
describing two-phonon cooling of the mechanical oscillator and show that for high temperatures
and weak coupling, the steady-state phonon number distribution is non-thermal (Gaussian).
Moreover, I will discuss systems where the position of the mechanical oscillator is coupled
parametrically to the cavity, but the equations cannot be linearized. One example is recent
experiments with ultracold atoms in optical resonators which have reached the regime where a
single photon displaces the mechanical oscillator by more than its zero-point uncertainty. I will
show how this can be detected by probing the outgoing light.
Some of these results I will present have been published in PRA 82, 021806(R) (2010).
15

RADIATION PRESSURE AT THE NANOSCALE: CLASSICAL AND
QUANTUM-OPTICAL APPLICATIONS
Oskar Painter
Thomas J. Watson, Sr., Laboratory of Applied Physics,
California Institute of Technology
In the last several years, rapid advances have been made in the field of cavity optomechanics, in
which the usually feeble radiation pressure force of light is used to manipulate (and precisely
monitor) mechanical motion. These advances have moved the field from the multi-km
interferometer of a gravitational wave observatory, to the optical table top, and now all the way
down to a silicon microchip. In this talk I will describe these advances, and discuss our own work
to realize radiation pressure within nanoscale structures in the form of photonic and phononic
crystals (dubbed optomechanical crystals) and coupled microring cavities. Applications of these
new nano-opto-mechanical systems include: all-optically tunable photonics, optically powered RF
and microwave oscillators, and precision force/acceleration and mass sensing. Additionally there
is the potential for these nanomechanical systems to be used in hybrid quantum networks,
enabling storage or transfer of quantum information between disparate quantum systems. I will
introduce several conceptual ideas regarding phonon-photon translation and slow light effects
which may be used in such quantum settings, and discuss recent experiments to realize them in
practice.
16

THE PHOTON BLOCKADE EFFECT IN OPTOMECHANICAL SYSTEMS
Peter Rabl
Iqoqi, Austrian Academy of Sciences
The implementation of strong optical non-linearities on a single photon level is one of the central
themes in quantum optics and over the past years many setting based on atomic cavity QED have
been discussed to achieve this goal. A very different type of light-matter interactions occurs in
optomechanical systems where photons are coupled to mechanical motion via radiation pressure
forces. Recent experiments have shown that the single photon strong coupling regime of
optomechanics is within reach and might open a completely new route towards non-linear
quantum optics. As a most pronounced signature of strong photon interactions I will discuss in
this talk the appearance of a photon blockade effect in weakly driven optomechanical systems. I
will show that an intuitive interpretation of this effect can be given in terms of displaced oscillator
states and identify the parameter regime which is required to observe non-classical anti-bunching
and photon blockade effects in experiments.
17

OPTICAL TRAPPING AND COOLING OF GLASS MICROSPHERES
Mark Raizen
University of Texas
In this talk I will report on our experiments with glass microspheres trapped in optical tweezers in
air and in vacuum. In the air experiments, we have measured for the first time the instantaneous
velocity of a Brownian particle, following a prediction by Albert Einstein from 1907. In our
experiments with a trapped microsphere in vacuum, we have cooled the center-of-mass motion to
1.5 mK, on the way towards ground-state cooling.
18

OPTOMECHANICAL MATTER-WAVE INTERFEROMETER FOR
MICROSPHERES
Oriol Romero-Isart
Max Planck Institute For
Quantum Optics
In this talk I will first review the proposal of using optically levitating objects for cavity quantum
optomechanics as well as some proposals to prepare and measure quantum superposition states.
Then, I will show how a matter-wave interferometer for microspheres can be realized using
optomechanics. This opens up the possibility to explore a new parameter regime in the mass of
the object (containing billions of atoms), and the size of the quantum superposition (orders of
magnitude larger than the ground state size) used in the interferometer. I will analyze its viability
under realistic experimental parameters and its potential application to provide unprecedented
bounds to objective collapse models of the wavefunction.
19

OPTOMECHANICS WITH A SILICON NITRIDE MEMBRANE
APPROACHING THE QUANTUM REGIME
Jack Sankey
Yale University
A major goal in optomechanics is to observe and control quantum behavior in a system consisting
of a solid mechanical element coupled to an optical cavity. Work toward this goal has traditionally
focused on increasing the strength of this coupling; however, the form of the coupling is crucial in
determining what phenomena are observable.
Here I will demonstrate that avoided crossings in the spectrum of an optical cavity containing a
flexible dielectric membrane allow us to realize several different forms of the optomechanical
coupling. These include cavity detunings that are (to lowest order) linear, quadratic, or quartic in
the membrane's displacement, and a cavity finesse that is linear in (or independent of) the
membrane's displacement. All the couplings are realized in a single device with extremely low
optical loss and can be tuned over a wide range in situ; in particular, we find that the quadratic
coupling can be increased three orders of magnitude beyond previous devices. As a result of these
advances, the device presented here should be capable of demonstrating the quantization of the
membrane's mechanical energy.
I will also discuss our recent efforts to laser cool the membrane's vibrations into the quantum
regime. By coupling free-space laser light from room temperature into a 300 mK cryostat we have
cooled the membrane's motion from a phonon occupancy of 30,000 to roughly 10. Using a
recently-implemented heterodyne measurement we hope to both extract signatures of quantum
behavior in the membrane's motion and measure a phonon occupancy close to zero.
20

CAVITY OPTOMECHANICS: BEYOND THE GROUND STATE
Swati Singh
University of Arizona
The talk will review some of our recent theoretical work in optomechanics, starting with a
discussion of an optical spring approach to ground state cooling, and then turning to more recent
work on the use of hybrid optomechanical systems as sensitive arrangements to induce and
quantify the back-action of quantum measurements on macroscopic systems. If time permits, I
will conclude with a presentation of novel methods to generate non-classical states in mechanical
cantilevers.
21

OPTOMECHANICAL COOLING AND AMPLIFICATION IN A CHIP-SCALE
INTEGRATED CIRCUIT
Hong Tang
Yale University
I will describe our efforts in developing integrated circuits of cavity optomechanics on a silicon
compatible chip. A progressive path for scaling optomechanical structures to smaller size, higher
frequency and stronger coupling will be presented. We will show several promising applications
stemming out on-chip cooling and amplification functions.
22

CIRCUIT CAVITY ELECTROMECHANICS IN THE STRONG
COUPLING REGIME
John Teufel
NIST – Boulder
In the longstanding endeavor to access the quantum nature of macroscopic mechanical motion,
the experimental challenge is not only that of state preparation, but also one of measurement.
The flourishing field of cavity opto- and electro-mechanics, in which an electromagnetic
resonance couples parametrically to a mechanical oscillator, addresses both of these challenges—
providing a nearly ideal architecture for both manipulation and detection of mechanical motion
at the quantum level. In this talk, I present experiments in which the motion of a high-Q,
micromechanical membrane couples to a superconducting microwave resonator. When the
circuit is excited with a coherent microwave tone near the cavity resonance, the displacement of
the oscillator becomes encoded as modulation of this tone. The microwaves, in turn, also impart
forces back on the oscillator which enforce the Heisenberg limits on measurement, and can also
be exploited to either cool or amplify the motion. The unprecedented electromechanical
coupling strength allows the driven system to enter the strong- coupling regime, where the normal
modes are now hybrids of the original radio-frequency mechanical and the microwave electrical
resonances. This normal-mode splitting is verified by direct spectroscopy of the ‘dressed states’ of
the hybridized cavity resonance, showing excellent agreement with theoretical predictions. As all
of these experiments take place in at a temperature below 40 mK, this system operates in the
quantum enabled regime where the thermal decoherence rate is small enough to allow sideband
cooling of the mechanical mode to the ground state. By measuring the noise spectrum of this
mechanical system with a nearly quantum-limited microwave amplifier, the residual thermal
motion of the oscillator is easily resolvable above the measurement imprecision. The final part of
this talk will quantify the thermal motion of the oscillator as it is cooled with radiation-pressure
forces to below its quantum zero-point motion and enters the strong coupling regime.
23

A PHONON-TUNNELING APPROACH TO CLAMPING LOSSES OF
MECHANICAL RESONATORS
Ignacio Wilson-Rae
Technische Universit ̈at M ̈unchen
State of the art optomechanical and nanomechanical setups are close to allowing for the
observation of quantum effects in a “macroscopic” mechanical system. A ma jor challenge that
remains to be addressed is understanding and controlling mechanical dissipation in these systems.
Here we analyze the dissipation mechanism induced by the unavoidable coupling of the resonator
to the substrate (known as clamping losses). We follow a Hamiltonian treatment and derive the
Caldeira-Leggett model that determines the quantum Brownian motion of a given resonance
starting from the elastic scattering eigenmodes of the entire structure including the substrate. Our
“phonon tunneling” approach provides the leading contribution in the aspect ratio or, more
generally, in kRd, where 1/kR is the characteristic length scale over which the resonator mode
varies appreciably and d the characteristic dimension of the contact area from which the
resonator is suspended. This yields a “master formula” for the dissipation 1/Q that is applicable
to a very wide range of high-Q resonators including planar structures (e.g. bridges), pedestal
geometries (e.g. microdisks), and single-walled carbon nanotubes (CNT). The resulting limits for
the Q-values have a strong geometric character.
This master formula for the dissipation, has allowed us to develop an efficient FEM-enabled
numerical method that can be used as an aid to design in order to minimize the clamping loss of
complex geometries. We apply this concept to free-free micromirror structures relevant for Fabry-
Perot based optomechanics. In addition, this design allows to isolate support-induced losses from
other dissipation channels. Thus, we perform a rigorous test of the theory developed and
demonstrate the strong geometric dependence of this loss mechanism. Furthermore, we analyze
the case of high-stress nanomechanical resonators and test the theory on Si3 N4 membranes with
circular and square geometries. The Q-values of different harmonics present a striking nonmonotonic
behavior which is successfully explained. For the circular geometry we identify a class
of modes for which destructive interference of the radiated waves leads to an exponential
suppression of the damping rate as the harmonic index is increased, rendering these modes
effectively clamping-loss free. This may provide a route towards ultra-high-Q nanomechanics and
is directly relevant to dispersive optomechanical setups utilizing a thin membrane. In addition to
furnishing reliable predictions for the design-limited Q, our approach allows to determine the
spectrum of the environment. This is relevant to analyze the quantum regime in scenarios where
the resonator is strongly coupled to an anharmonic system or exhibits strong nonlinearity.
24

RADIATION PRESSURE AND QUANTUM NOISE
Christopher Wipf
Massachusetts Institute of Technology
Laser Interferometer Gravitational-Wave Observatory
In LIGO, optomechanical displacement sensing at the quantum limit is needed in order to meet
the challenge of observing gravitational waves. Optical forces play an important role in this limit,
determining both the classical dynamics and the noise properties of the system. I will discuss
experiments underway in our lab, aimed at revealing these classical and quantum radiation
pressure effects.
25

HYBRID SYSTEMS: ATOMS AND OPTO-NANOMECHANICS
Peter Zoller
Institute for Theoretical Physics, University of Innsbruck
Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
We discuss a range of problems considering the interaction of atomic ensembles in free space and
inside cavities with opto-nanomechanical oscillators. Topics to be discussed include: Optical
lattices with micromechanical mirrors [1], strong coupling of a single atom to an oscillator in
CQED [2,3], and establishing continuous variable EPR correlations between atomic ensembles and
a opto-nanomechanical system [4].
References:
[1] K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, and T. W.
Hänsch, Phys. Rev. A 82, 021803(R) (2010)
[2] M. Wallquist, K. Hammerer, P. Zoller, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, J. Ye, and
H. J. Kimble, Phys. Rev. A 81, 023816 (2010)
[3] K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and
H. J. Kimble Phys. Rev. Lett. 103, 063005 (2009)
[4] K. Hammerer, M. Aspelmeyer, E. S. Polzik, and P. Zoller, Phys. Rev. Lett. 102, 020501 (2009)
26

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