Quantum cooperativity is evident in lightmatter platforms where quantumemitter ensembles are interfaced
with confined optical modes and are coupled via the ubiquitous electromagnetic quantum vacuum.
Cooperative effects can find applications, among other areas, in topological quantum optics, in quantum
metrology, or in quantum information. This tutorial provides a set of theoretical tools to tackle the behavior
responsible for the onset of cooperativity by extending open quantum system dynamics methods, such as
the master equation and quantum Langevin equations, to electronphoton interactions in strongly coupled
and correlated quantumemitter ensembles. The methods are illustrated on a wide range of current research
topics such as the design of nanoscale coherentlight sources, highly reflective quantum metasurfaces, or
low intracavity power superradiant lasers.
Phase synchronization in dissipative nonHermitian coupled quantum systems
We study the interplay between nonHermitian dynamics and phase synchronization in a system of N bosonic modes coupled to an auxiliary mode. The linearity of the evolution in such a system allows for the derivation of fully analytical results for synchronization conditions. In contrast, analysis at the level of phase dynamics, followed by a transformation to a collective basis allows a complete reduction to an alltoall coupled Kuramoto model with known analytical solutions. We provide analytical and numerical solutions for systems ranging from a few modes to the macroscopic limit of large N in the presence of inhomogeneous frequency broadening and test the robustness of phase synchronization under the action of external noise.
Molecular polaritonics in dense mesoscopic disordered ensembles
Christian Sommer, Michael Reitz, Francesca Mineo, Claudiu Genes
Physical Review Research
3(3)
033141
(2021)

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We study the dependence of the vacuum Rabi splitting (VRS) on frequency disorder, vibrations, nearfield effects, and density in molecular polaritonics. In the mesoscopic limit, static frequency disorder alone can already introduce a loss mechanism from polaritonic states into a dark state reservoir, which we quantitatively describe, providing an analytical scaling of the VRS with the level of disorder. Disorder additionally can split a molecular ensemble into donortype and acceptortype molecules and the combination of vibronic coupling, dipoledipole interactions, and vibrational relaxation induces an incoherent FRET (Förster resonance energy transfer) migration of excitations within the collective molecular state. This is equivalent to a dissipative disorder and has the effect of saturating and even reducing the VRS in the mesoscopic, highdensity limit. Overall, this analysis allows to quantify the crucial role played by dark states in cavity quantum electrodynamics with mesoscopic, disordered ensembles.
Excitation transport with collective radiative decay
We investigate a onedimensional quantum emitter chain where transport of excitations and correlations takes place via nearest neighbor, dipoledipole interactions. In the presence of collective radiative emission, we show that a phase imprinting wavepacket initialization procedure can lead to subradiant transport and can preserve quantum correlations. In the context of cavity mediated transport, where emitters are coupled to a common delocalized optical mode, we analyze the effect of frequency disorder and nonidentical photonemitter couplings on excitation transport.
Floquet engineering of molecular dynamics via infrared coupling
Michael Reitz, Claudiu Genes
The Journal of Chemical Physics
153
234305
(2020)

Journal
We discuss Floquet engineering of dissipative molecular systems through periodic driving of an infraredactive vibrational transition, either directly or via a cavity mode. Following a polaron quantum Langevin equations approach, we derive correlation functions and stationary quantities showing strongly modified optical response
of the infrareddressed molecule. The coherent excitation of molecular vibrational modes, in combination with the modulation of electronic degrees of freedom due to vibronic coupling can lead to both enhanced
vibronic coherence as well as control over vibrational sideband amplitudes. The additional coupling to an infrared cavity allows for the controlled suppression of undesired sidebands, an effect stemming from the Purcell enhancement of vibrational relaxation rates.
Multimode colddamping optomechanics with delayed feedback
Christian Sommer, Alekhya Ghosh, Claudiu Genes
Physical Review Research
2
033299
(2020)

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We investigate the role of time delay in colddamping optomechanics with multiple mechanical resonances.
For instantaneous electronic response, it was recently shown by C. Sommer and C. Genes [Phys. Rev. Lett. 123,
203605 (2019)] that a single feedback loop is sufficient to simultaneously remove thermal noise from many
mechanical modes. While the intrinsic delayed response of the electronics can induce singlemode and mutual
heating between adjacent modes, we propose to counteract such detrimental effects by introducing an additional
time delay to the feedback loop. For lossy cavities and broadband feedback, we derive analytical results for the
final occupancies of the mechanical modes within the formalism of quantum Langevin equations. For modes
that are frequency degenerate collective effects dominate, mimicking behavior similar to Dicke super and
subradiance. These analytical results, corroborated with numerical simulations of both transient and steady state
dynamics, allow us to find suitable conditions and strategies for efficient singlemode or multimode feedback
optomechanics.
Moleculephoton interactions in phononic environments
Michael Reitz, Christian Sommer, Burak Gürlek, Vahid Sandoghdar, DiegoMartin Cano, Claudiu Genes
Physical Review Research
2
033270
(2020)

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Molecules constitute compact hybrid quantum optical systems that can interface photons, electronic degrees of freedom, localized mechanical vibrations, and phonons. In particular, the strong vibronic interaction between electrons and nuclear motion in a molecule resembles the optomechanical radiation pressure Hamiltonian. While molecular vibrations are often in the ground state even at elevated temperatures, one still needs to get a handle on decoherence channels associated with phonons before an efficient quantum optical network based on optovibrational interactions in solidstate molecular systems could be realized. As a step towards a better understanding of decoherence in phononic environments, we take here an open quantum system approach to the nonequilibrium dynamics of guest molecules embedded in a crystal, identifying regimes of Markovian versus nonMarkovian vibrational relaxation. A stochastic treatment, based on quantum Langevin equations, predicts collective vibronvibron dynamics that resembles processes of sub and superradiance for radiative transitions. This in turn leads to the possibility of decoupling intramolecular vibrations from the phononic bath, allowing for enhanced coherence times of collective vibrations. For molecular polaritonics in strongly confined geometries, we also show that the imprint of optovibrational couplings onto the emerging output field results in effective polariton crosstalk rates for finite bath occupancies.
Ising model in a lightinduced quantized transverse field
Jonas Rohn, Max Hörmann, Claudiu Genes, Kai Phillip Schmidt
Physical Review Research
2
023131
(2020)

Journal
We investigate the influence of lightmatter interactions on correlated quantum matter by studying the
paradigmatic DickeIsing model. This type of coupling to a confined, spatially delocalized bosonic light mode,
such as provided by an optical resonator, resembles a quantized transverse magnetic field of tunable strength. As
a consequence, the symmetrybroken magnetic state breaks down for strong enough lightmatter interactions to
a paramagnetic state. The nonlocal character of the bosonic mode can change the quantum phase transition in
a drastic manner, which we analyze quantitatively for the simplest case of the DickeIsing chain geometry.
The results show a direct transition between a magnetically ordered phase with zero photon density and a
magnetically polarized phase with superradiant behavior of the light. Our predictions are equally valid for the
dual quantized Ising chain in a conventional transverse magnetic field.
Ensembleinduced strong lightmatter coupling of a single quantum emitter
Stefan Schütz, Johannes Schachenmayer, David Hagenmüller, Gavin K. Brennen, Thomas Volz, Vahid Sandoghdar, Thomas W. Ebbesen, Claudiu Genes, Guido Pupillo
We discuss a technique to strongly couple a single target quantum emitter to a cavity mode, which is enabled by virtual excitations of a nearby mesoscopic ensemble of emitters. A collective coupling of the latter to both the cavity and the target emitter induces strong photon nonlinearities in addition to polariton formation, in contrast to common schemes for ensemble strong coupling. We demonstrate that strong coupling at the level of a single emitter can be engineered via coherent and dissipative dipolar interactions with the ensemble, and provide realistic parameters for a possible implementation with
SiV− defects in diamond. Our scheme can find applications, amongst others, in quantum information processing or in the field of cavityassisted quantum chemistry.
Prospects of reinforcement learning for the simultaneous damping of many mechanical modes
Christian Sommer, Muhammad Asjad, Claudiu Genes
Scientific Reports
10(2623)
(2020)

Journal

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We apply adaptive feedback for the partial refrigeration of a mechanical resonator, i.e. with the aim to
simultaneously cool the classical thermal motion of more than one vibrational degree of freedom. The
feedback is obtained from a neural network parametrized policy trained via a reinforcement learning
strategy to choose the correct sequence of actions from a fnite set in order to simultaneously reduce
the energy of many modes of vibration. The actions are realized either as optical modulations of the
spring constants in the socalled quadratic optomechanical coupling regime or as radiation pressure
induced momentum kicks in the linear coupling regime. As a proof of principle we numerically illustrate
efcient simultaneous cooling of four independent modes with an overall strong reduction of the total
system temperature.
Partial optomechanical refrigeration via multimode colddamping feedback
We provide a fully analytical treatment for the partial refrigeration of the thermal motion of a quantum mechanical resonator under the action of feedback. As opposed to standard cavity optomechanics where the aim is to isolate and cool a single mechanical mode, the aim here is to extract the thermal energy from many vibrational modes within a large frequency bandwidth. We consider a standard colddamping technique, where homodyne readout of the cavity output field is fed into a feedback loop that provides a cooling action directly applied on the mechanical resonator. Analytical and numerical results predict that low final occupancies are achievable independent of the number of modes addressed by the feedback, as long as the cooling rate is smaller than the intermode frequency separation. For resonators exhibiting a few nearly degenerate pairs of modes, cooling is less efficient and a weak dependence on the number of modes is obtained. These scalings hint toward the design of frequencyresolved mechanical resonators, where efficient refrigeration is possible via simultaneous colddamping feedback.
Laser refrigeration of gas filled hollowcore fibres
Christian Sommer, Nicolas Y. Joly, Helmut Ritsch, Claudiu Genes
We evaluate prospects, performance and temperature limits of a new approach to macroscopic scale laser refrigeration. The considered
refrigeration device is based on exciplexmediated frequency upconversion inside hollowcore fibers pressurized with a dopant  buffer
gas mixture. Exciplexes are excited molecular states formed by two atoms (dopant and buffer) which do not form a molecule in the
ground state but exhibit bound states for electronically excited states. The cooling cycle consists of absorption of laser photons during
atomic collisions inducing light assisted exciplex formation followed by blueshifted spontaneous emission on the atomic line of the bare
dopant atoms after molecular separation. This process, closely related to reversing the gain mechanism in excimer lasers, allows for a large
fraction of collision energy to be extracted in each cycle. The hollowcore fiber plays a crucial role as it allows for strong lightmatter
interactions over a long distance, which maximizes the cooling rate per unit volume and the cooling efficiency per injected photon while
limiting reabsorption of spontaneously emitted photons channeled into unguided radiation modes. Using quantum optical rate equations
and refined dynamical simulations we derive general conditions for efficient cooling of both the gas and subsequently of the surrounding
solid state environment. Our analytical approach is applicable to any specific exciplex system considered and reveals the shape of the
exciplex potential landscapes as well as the density of the dopant as crucial tuning knobs. The derived scaling laws allow for the identification
of optimal exciplex characteristics that help to choose suitable gas mixtures that maximize the refrigeration efficiency for specific
applications.
Cavity Quantum Electrodynamics with FrequencyDependent Reflectors
We present a general framework for cavity quantum electrodynamics with strongly frequencydependent mirrors. The method is applicable to a variety of reflectors exhibiting sharp internal resonances as can be realized, for example, with photoniccrystal mirrors or with twodimensional atomic arrays around subradiant points. Our approach is based on a modification of the standard inputoutput formalism to explicitly include the dynamics of the mirror’s internal resonance. We show how to directly extract the interaction parameters from the comparison with classical transfer matrix theory and how to treat the nonMarkovian dynamics of the cavity field mode introduced by the mirror’s internal resonance. As an application within optomechanics, we illustrate how a nonMarkovian Fanoresonance cavity with a flexible photoniccrystal mirror can provide both sideband resolution as well as strong heating suppression in optomechanical cooling. This approach, amenable to a wide range of systems, opens up possibilities for using hybrid frequencydependent reflectors in cavity quantum electrodynamics for engineering novel forms of lightmatter interactions.
Langevin Approach to Quantum Optics with Molecules
We investigate the interaction between light and molecular systems modeled as quantum emitters coupled to a multitude of vibrational modes via a Holsteintype interaction. We follow a quantum Langevin equations approach that allows for analytical derivations of absorption and fluorescence profiles of molecules driven by classical fields or coupled to quantized optical modes. We retrieve analytical expressions for the modification of the radiative emission branching ratio in the Purcell regime and for the asymmetric cavity transmission associated with dissipative cross talk between upper and lower polaritons in the strong coupling regime. We also characterize the Förster resonance energy transfer process between donoracceptor molecules mediated by the vacuum or by a cavity mode.
Enhanced collective Purcell effect of coupled quantum emitter systems
David Plankensteiner, Christian Sommer, Michael Reitz, Helmut Ritsch, Claudiu Genes
Cavityembedded quantum emitters show strong modifications of free space radiation properties such as an enhanced decay known as the Purcell effect. The central parameter is the cooperativity C  the ratio of the square of the coherent cavity coupling strength over the product of cavity and emitter decay rates. For a single emitter, C is independent of the transition dipole moment and dictated by geometric cavity properties such as finesse and mode waist. In a recent work Phys. Rev. Lett. 119, 093601 (2017) we have shown that collective excitations in ensembles of dipoledipole coupled quantum emitters show a disentanglement between the coherent coupling to the cavity mode and spontaneous free space decay. This leads to a strong enhancement of the cavity cooperativity around certain collective subradiant antiresonances. Here, we present a quantum Langevin equations approach aimed at providing results beyond the classical coupled dipoles model. We show that the subradiantly enhanced cooperativity imprints its effects onto the cavity output field quantum correlations while also strongly increasing the cavityemitter system's collective Kerr nonlinear effect.
Super and subradiance of clock atoms in multimode optical waveguides
Laurin Ostermann, Clément Meignant, Claudiu Genes, Helmut Ritsch
The transversely confined propagating modes of an optical fiber mediate virtually infinite range energy exchanges among atoms placed within their field, which adds to the inherent free space dipole–dipole coupling. Typically, the single atom free space decay rate largely surpasses the emission rate into the guided fiber modes. However, scaling up the atom number as well as the system size amounts to entering a collective emission regime, where fiberinduced superradiant spontaneous emission dominates over free space decay. We numerically study this super and subradiant decay of highly excited atomic states for one or several transverse fiber modes as present in hollow core fibers. As particular excitation scenarios we compare the decay of a totally inverted state to the case of π/2 pulses applied transversely or along the fiber axis as in standard Ramsey or Rabi interferometry. While a mean field approach fails to correctly describe the initiation of superradiance, a secondorder approximation accounting for pairwise atom–atom quantum correlations generally proves sufficient to reliably describe superradiance of ensembles from two to a few hundred particles. In contrast, a full account of subradiance requires the inclusion of all higher order quantum correlations. Considering multiple guided modes introduces a natural effective cutoff for the interaction range emerging from the dephasing of different fiber contributions.
Interference effects in hybrid cavity optomechanics
Ondrej Černotík, Claudiu Genes, Aurelien Dantan
Quantum Science and Technology
4(2)
024002
(2019)

Journal

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Radiation pressure forces in cavity optomechanics allow for efficient cooling of vibrational modes of macroscopic mechanical resonators, the manipulation of their quantum states, as well as generation of optomechanical entanglement. The standard mechanism relies on the cavity photons directly modifying the state of the mechanical resonator. Hybrid cavity optomechanics provides an alternative approach by coupling mechanical objects to quantum emitters, either directly or indirectly via the common interaction with a cavity field mode. While many approaches exist, they typically share a simple effective description in terms of a single force acting on the mechanical resonator. More generally, one can study the interplay between various forces acting on the mechanical resonator in such hybrid mechanical devices. This interplay can lead to interference effects that may, for instance, improve cooling of the mechanical motion or lead to generation of entanglement between various parts of the hybrid device. Here, we provide such an example of a hybrid optomechanical system where an ensemble of quantum emitters is embedded into the mechanical resonator formed by a vibrating membrane. The interference between the radiation pressure force and the mechanically modulated TavisCummings interaction leads to enhanced cooling dynamics in regimes in which neither force is efficient by itself. Our results pave the way towards engineering novel optomechanical interactions in hybrid optomechanical systems.
Ramsey interferometry of Rydberg ensembles inside microwave cavities
Christian Sommer, Claudiu Genes
JOURNAL OF PHYSICS BATOMIC MOLECULAR AND OPTICAL PHYSICS
51(11)
115502
(2018)

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We study ensembles of Rydberg atoms in a confined electromagnetic environment such as is provided by a microwave cavity. The competition between standard free space Ising type and cavitymediated interactions leads to the emergence of different regimes where the particle particle couplings range from the typical van der Waals r(6) behavior to r(3) and to rindependence. We apply a Ramsey spectroscopic technique to map the twobody interactions into a characteristic signal such as intensity and contrast decay curves. As opposed to previous treatments requiring highdensities for considerable contrast and phase decay (Takei et al 2016 Nat. Comms. 7 13449; Sommer et al 2016 Phys. Rev. A 94 053607), the cavity scenario can exhibit similar behavior at much lower densities.
Energy transfer and correlations in cavityembedded donoracceptor configurations
The rate of energy transfer in donoracceptor systems can be manipulated via the common interaction with the confined electromagnetic modes of a microcavity. We analyze the competition between the nearfield short range dipoledipole energy exchange processes and the cavity mediated longrange interactions in a simplified model consisting of effective twolevel quantum emitters that could be relevant for molecules in experiments under cryogenic conditions. We find that freespace collective incoherent interactions, typically associated with suband superradiance, can modify the traditional resonant energy transfer scaling with distance. The same holds true for cavitymediated collective incoherent interactions in a weakcoupling but strongcooperativity regime. In the strong coupling regime, we elucidate the effect of pumping into cavity polaritons and analytically identify an optimal energy flow regime characterized by equal donor/acceptor Hopfield coefficients in the middle polariton. Finally we quantify the buildup of quantum correlations in the donoracceptor system via the twoqubit concurrence as a measure of entanglement.
Cavityassisted mesoscopic transport of fermions: Coherent and dissipative dynamics
David Haggenmüller, Stefan Schütz, Johannes Schachenmayer, Claudiu Genes, Guido Pupillo
We study the interplay between charge transport and lightmatter interactions in a confined geometry by considering an open, mesoscopic chain of twoorbital systems resonantly coupled to a single bosonic mode close to its vacuum state. We introduce and benchmark different methods based on selfconsistent solutions of nonequilibrium Green's functions and numerical simulations of the quantum master equation, and derive both analytical and numerical results. It is shown that in the dissipative regime where the cavity photon decay rate is the largest parameter, the lightmatter coupling is responsible for a steadystate current enhancement scaling with the cooperativity parameter. We further identify different regimes of interest depending on the ratio between the cavity decay rate and the electronic bandwidth. Considering the situation where the lower band has a vanishing bandwidth, we show that for a highfinesse cavity, the properties of the resonant Bloch state in the upper band are transferred to the lower one, giving rise to a delocalized state along the chain. Conversely, in the dissipative regime with lowcavity quality factors, we find that the current enhancement is due to a collective decay of populations from the upper to the lower band.
Cavity Antiresonance Spectroscopy of Dipole Coupled Subradiant Arrays
David Plankensteiner, Christian Sommer, Helmut Ritsch, Claudiu Genes
An array of N closely spaced dipole coupled quantum emitters exhibits superand subradiance with characteristic tailorable spatial radiation patterns. Optimizing the emitter geometry and distance with respect to the spatial profile of a near resonant optical cavity mode allows us to increase the ratio between light scattering into the cavity mode and free space emission by several orders of magnitude. This leads to distinct scaling of the collective coherent emitterfield coupling vs the free space decay as a function of the emitter number. In particular, for subradiant states, the effective cooperativity increases much faster than the typical linear proportional to N scaling for independent emitters. This extraordinary collective enhancement is manifested both in the amplitude and the phase profile of narrow collective antiresonances appearing at the cavity output port in transmission spectroscopy.
Lightmatter interactions in multielement resonators
Claudiu Genes, Aurelien Dantan
JOURNAL OF PHYSICS BATOMIC MOLECULAR AND OPTICAL PHYSICS
50(10)
105502
(2017)

Journal
We investigate lightmatter interactions in multielement optical resonators and provide a roadmap for the identification of structural resonances and the description of the interaction of single extended cavity modes with quantum emitters or mechanical resonators. Using a first principle approach based on the transfer matrix formalism we analyze, both numerically and analytically, the static and dynamical properties of threeand fourmirror cavities. We investigate in particular conditions under which the confinement of the field in specific subcavities allows for enhanced lightmatter interactions in the context of cavity quantum electrodynamics and cavity optomechanics.
CavityEnhanced Transport of Charge
David Hagenmueller, Johannes Schachenmayer, Stefan Schutz, Claudiu Genes, Guido Pupillo
We theoretically investigate charge transport through electronic bands of a mesoscopic onedimensional system, where interband transitions are coupled to a confined cavity mode, initially prepared close to its vacuum. This coupling leads to lightmatter hybridization where the dressed fermionic bands interact via absorption and emission of dressed cavity photons. Using a selfconsistent nonequilibrium Green's function method, we compute electronic transmissions and cavity photon spectra and demonstrate how lightmatter coupling can lead to an enhancement of charge conductivity in the steady state. We find that depending on cavity loss rate, electronic bandwidth, and coupling strength, the dynamics involves either an individual or a collective response of Bloch states, and we explain how this affects the current enhancement. We show that the charge conductivity enhancement can reach orders of magnitudes under experimentally relevant conditions.
Laser noise imposed limitations of ensemble quantum metrology
D. Plankensteiner, J. Schachenmayer, H. Ritsch, Claudiu Genes
JOURNAL OF PHYSICS BATOMIC MOLECULAR AND OPTICAL PHYSICS
49(24)
245501
(2016)

Journal

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Laser noise is a decisive limiting factor in high precision spectroscopy of narrow lines using atomic ensembles. In an idealized Doppler and differentiallightshiftfree magic wavelength lattice configuration, it remains as one distinct principal limitation beyond collective atomic decay. In this work we study the limitations originating from laser phase and amplitude noise in an idealized Ramsey pulse interrogation scheme with uncorrelated atoms. Phase noise leads to a saturation of the frequency sensitivity with increasing atom number while amplitude noise implies a scaling 1/root T with T being the interrogation time. We employ a technique using decoherencefree subspaces first introduced in Dorner (2012 New J. Phys. 14 043011) which can restore the scaling with the square root of the inverse particle number 1/root N. Similar results and improvements are obtained numerically for a Rabi spectroscopy setup.
Direct observation of ultrafast manybody electron dynamics in an ultracold Rydberg gas
NATURE COMMUNICATIONS
7
13449
(2016)

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PDF
Manybody correlations govern a variety of important quantum phenomena such as the emergence of superconductivity and magnetism. Understanding quantum manybody systems is thus one of the central goals of modern sciences. Here we demonstrate an experimental approach towards this goal by utilizing an ultracold Rydberg gas generated with a broadband picosecond laser pulse. We follow the ultrafast evolution of its electronic coherence by timedomain Ramsey interferometry with attosecond precision. The observed electronic coherence shows an ultrafast oscillation with a period of 1 femtosecond, whose phase shift on the attosecond timescale is consistent with manybody correlations among Rydberg atoms beyond meanfield approximations. This coherent and ultrafast manybody dynamics is actively controlled by tuning the orbital size and population of the Rydberg state, as well as the mean atomic distance. Our approach will offer a versatile platform to observe and manipulate nonequilibrium dynamics of quantum manybody systems on the ultrafast timescale.
Timedomain Ramsey interferometry with interacting Rydberg atoms
We theoretically investigate the dynamics of a gas of strongly interacting Rydberg atoms subject to a timedomain Ramsey interferometry protocol. The manybody dynamics is governed by an Isingtype Hamiltonian with longrange interactions of tunable strength. We analyze and model the contrast degradation and phase accumulation of the Ramsey signal and identify scaling laws for varying interrogation times, ensemble densities, and ensemble dimensionalities.
Selective protected state preparation of coupled dissipative quantum emitters
D. Plankensteiner, L. Ostermann, H. Ritsch, Claudiu Genes
Inherent binary or collective interactions in ensembles of quantum emitters induce a spread in the energy and lifetime of their eigenstates. While this typically causes fast decay and dephasing, in many cases certain special entangled collective states with minimal decay can be found, which possess ideal properties for spectroscopy, precision measurements or information storage. We show that for a specific choice of laser frequency, power and geometry or a suitable configuration of control fields one can efficiently prepare these states. We demonstrate this by studying preparation schemes for strongly subradiant entangled states of a chain of dipoledipole coupled emitters. The prepared state fidelity and its entanglement depth is further improved via spatial excitation phase engineering or tailored magnetic fields.
Conductivity in organic semiconductors hybridized with the vacuum field
E. Orgiu, J. George, J. A. Hutchison, E. Devaux, J. F. Dayen, B. Doudin, F. Stellacci, C. Genet, J. Schachenmayer, et al.
Much effort over the past decades has been focused on improving carrier mobility in organic thinfilm transistors by optimizing the organization of the material or the device architecture. Here we take a different path to solving this problem, by injecting carriers into states that are hybridized to the vacuum electromagnetic field. To test this idea, organic semiconductors were strongly coupled to plasmonic modes to form coherent states that can extend over as many as 105 molecules and should thereby favour conductivity. Experiments show that indeed the current does increase by an order of magnitude at resonance in the coupled state, reflecting mostly a change in fieldeffect mobility. A theoretical quantum model confirms the delocalization of thewavefunctions of the hybridized states and its effect on the conductivity. Our findings illustrate the potential of engineering the vacuum electromagnetic environment to modify and to improve properties of materials.
A Realization of a QuasiRandom Walk for Atoms in TimeDependent Optical Potentials
We consider the time dependent dynamics of an atom in a twocolor pumped cavity, longitudinally through a side mirror and transversally via direct driving of the atomic dipole. The beating of the two driving frequencies leads to a time dependent effective optical potential that forces the atom into a nontrivial motion, strongly resembling a discrete random walk behavior between lattice sites. We provide both numerical and analytical analysis of such a quasirandom walk behavior.
CavityEnhanced Transport of Excitons
Johannes Schachenmayer, Claudiu Genes, Edoardo Tignone, Guido Pupillo
We show that excitontype transport in certain materials can be dramatically modified by their inclusion in an optical cavity: the modification of the electromagnetic vacuum mode structure introduced by the cavity leads to transport via delocalized polariton modes rather than through tunneling processes in the material itself. This can help overcome exponential suppression of transmission properties as a function of the system size in the case of disorder and other imperfections. We exemplify massive improvement of transmission for excitonic wave packets through a cavity, as well as enhancement of steadystate exciton currents under incoherent pumping. These results may have implications for experiments of exciton transport in disordered organic materials. We propose that the basic phenomena can be observed in quantum simulators made of Rydberg atoms, cold molecules in optical lattices, as well as in experiments with trapped ions.
Transmissive optomechanical platforms with engineered spatial defects
Linear optomechanical photonphonon couplings in the membraneinthemiddle setup can be enhanced by taking a multielement approach as it was recently shown [A. Xuereb, C. Genes, and A. Dantan, Phys. Rev. Lett. 109, 223601 ( 2012)]. The particular example considered consists of a periodic array of membranes embedded in a highfinesse optical cavity and operating in the transmissive regime, i.e., around resonances of the compound cavitymembrane system. Here we propose further improvements in such a setup by breaking the translational invariance of the array, i.e., by considering quasiperiodic arrays with engineered quadratic spatial defects in the membrane positions. The localization of light modes induced by the defect combined with the access of the aforementioned transmissive regime window can lead to additional enhancement of the strength of both linear and quadratic optomechanical couplings.
Protected subspace Ramsey spectroscopy
L. Ostermann, D. Plankensteiner, H. Ritsch, Claudiu Genes
We study a modified Ramsey spectroscopy technique employing slowly decaying states for quantum metrology applications using dense ensembles. While closely positioned atoms exhibit superradiant collective decay and dipoledipole induced frequency shifts, recent results [L. Ostermann, H. Ritsch, and C. Genes, Phys. Rev. Lett. 111, 123601 (2013)] suggest the possibility to suppress such detrimental effects and achieve an even better scaling of the frequency sensitivity with interrogation time than for noninteracting particles. Here we present an indepth analysis of this "protected subspace Ramsey technique" using improved analytical modeling and numerical simulations including larger threedimensional (3D) samples. Surprisingly we find that using subradiant states of N particles to encode the atomic coherence yields a scaling of the optimal sensitivity better than 1/root N . Applied to ultracold atoms in 3D optical lattices we predict a precision beyond the single atom linewidth.
We investigate the dynamics of a mechanical resonator in which is embedded an ensemble of twolevel systems interacting with an optical cavity field. We show that this hybrid approach to optomechanics allows for enhanced effective interactions between the mechanics and the cavity field, leading, for instance, to groundstate cooling of the mechanics, even in regimes, like the unresolved sideband regime, in which standard radiation pressure cooling would be inefficient.
Reconfigurable LongRange Phonon Dynamics in Optomechanical Arrays
Andre Xuereb, Claudiu Genes, Guido Pupillo, Mauro Paternostro, Aurelien Dantan
We investigate periodic optomechanical arrays as reconfigurable platforms for engineering the coupling between multiple mechanical and electromagnetic modes and for exploring manybody phonon dynamics. Exploiting structural resonances in the coupling between light fields and collective motional modes of the array, we show that tunable effective longrange interactions between mechanical modes can be achieved. This paves the way towards the implementation of controlled phononic walks and heat transfer on densely connected graphs as well as the coherent transfer of excitations between distant elements of optomechanical arrays.
Nonclassical States of Light and Mechanics
Klemens Hammerer, Claudiu Genes, David Vitali, Paolo Tombesi, Gerard Milburn, Christoph Simon, Dirk Bouwmeester
Quantum Science and Technology
(2014)

Book Chapter
This chapter reports on theoretical protocols for generating nonclassical states of light and mechanics. Nonclassical states are understood as squeezed states, entangled states or states with negativeWigner function, and the nonclassicality can refer either to light, to mechanics, or to both, light and mechanics. In all protocols nonclassicality arises from a strong optomechanical coupling. Some protocols rely in addition on homodyne detection or photon counting of light.
Hybrid Mechanical Systems
Philipp Treutlein, Claudiu Genes, Klemens Hammerer, Martino Poggio, Peter Rabl
Quantum Science and Technology
(2014)

Book Chapter
We discuss hybrid systems in which a mechanical oscillator is coupled to another (microscopic) quantum system, such as trapped atoms or ions, solidstate spin qubits, or superconducting devices. We summarize and compare different coupling schemes and describe first experimental implementations. Hybrid mechanical systems enable new approaches to quantum control of mechanical objects, precision sensing, and quantum information processing.
Collectively enhanced optomechanical coupling in periodic arrays of scatterers
We investigate the optomechanical properties of a periodic array of identical scatterers placed inside an optical cavity and extend our previous results [Xuereb, Genes, and Dantan, Phys. Rev. Lett. 109, 223601 (2012)]. We show that operating at the points where the array is transmissive results in linear optomechanical coupling strengths between the cavity field and collective motional modes of the array that may be several orders of magnitude larger than is possible with an equivalent reflective ensemble. We describe and interpret these effects in detail and investigate the nature of the scaling laws of the coupling strengths for the different transmissive points in various regimes.
Enhanced optomechanical readout using optical coalescence
Claudiu Genes, Andre Xuereb, Guido Pupillo, Aurelien Dantan
We present a scheme to strongly enhance the readout sensitivity of the squared displacement of a mobile scatterer placed in a FabryPerot cavity. We investigate the largely unexplored regime of cavity electrodynamics in which a highly reflective element positioned between the end mirrors of a symmetric FabryPerot resonator strongly modifies the cavity response function, such that two longitudinal modes with different spatial parity are brought close to frequency degeneracy and interfere in the cavity output field. In the case of a movable middle reflector we show that the interference in this generic "optical coalescence" phenomenon gives rise to an enhanced frequency shift of the peaks of the cavity transmission that can be exploited in optomechanics.
Protected State Enhanced Quantum Metrology with Interacting TwoLevel Ensembles
Ramsey interferometry is routinely used in quantum metrology for the most sensitive measurements of optical clock frequencies. Spontaneous decay to the electromagnetic vacuum ultimately limits the interrogation time and thus sets a lower bound to the optimal frequency sensitivity. In dense ensembles of twolevel systems, the presence of collective effects such as superradiance and dipoledipole interaction tends to decrease the sensitivity even further. We show that by a redesign of the Ramseypulse sequence to include different rotations of individual spins that effectively fold the collective state onto a state close to the center of the Bloch sphere, partial protection from collective decoherence is possible. This allows a significant improvement in the sensitivity limit of a clock transition detection scheme over the conventional Ramsey method for interacting systems and even for noninteracting decaying atoms.
Quantumcorrelated motion and heralded entanglement of distant
optomechanically coupled objects
Wolfgang Niedenzu, Raimar M. Sandner, Claudiu Genes, Helmut Ritsch
JOURNAL OF PHYSICS BATOMIC MOLECULAR AND OPTICAL PHYSICS
45(24)
245501
(2012)

Journal
The motion of two distant trapped particles or mechanical oscillators can be strongly coupled by light modes in a high finesse optical resonator. In a two mode ring cavity geometry, trapping, cooling and coupling is implemented by the same modes. While the cosine mode provides for trapping, the sine mode facilitates ground state cooling and mediates nonlocal interactions. For classical point particles the centreofmass mode is strongly damped and the individual momenta get anticorrelated. Surprisingly, quantum fluctuations induce the opposite effect of positivelycorrelated particle motion, which close to zero temperature generates entanglement. The nonclassical correlations and entanglement are dissipationinduced and particularly strong after detection of a scattered photon in the sine mode. This allows for heralded entanglement by postselection. Entanglement is concurrent with squeezing of the particle distance and relative momenta, while the centreofmass observables acquire larger uncertainties.
Strong Coupling and LongRange Collective Interactions in Optomechanical Arrays
We investigate the collective optomechanics of an ensemble of scatterers inside a FabryPerot resonator and identify an optimized configuration where the ensemble is transmissive, in contrast to the usual reflective optomechanics approach. In this configuration, the optomechanical coupling of a specific collective mechanical mode can be several orders of magnitude larger than the singleelement case, and longrange interactions can be generated between the different elements since light permeates throughout the array. This new regime should realistically allow for achieving strong singlephoton optomechanical coupling with massive resonators, realizing hybrid quantum interfaces, and exploiting collective longrange interactions in arrays of atoms or mechanical oscillators.
Atommembrane cooling and entanglement using cavity electromagnetically induced transparency
Claudiu Genes, Helmut Ritsch, Michael Drewsen, Aurelien Dantan
We investigate a hybrid optomechanical system composed of a micromechanical oscillator as a movable membrane and an atomic threelevel ensemble within an optical cavity. We show that a suitably tailored cavity field response via electromagnetically induced transparency (EIT) in the atomic medium allows for strong coupling of the membrane's mechanical oscillations to the collective atomic groundstate spin. This facilitates groundstate cooling of the membrane motion, quantum state mapping, and robust atommembrane entanglement even for cavity widths larger than the mechanical resonance frequency.
Optical lattices with micromechanical mirrors
K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Haensch
We investigate a setup where a cloud of atoms is trapped in an optical lattice potential of a standingwave laser field which is created by retroreflection on a micromembrane. The membrane vibrations itself realize a quantum mechanical degree of freedom. We show that the centerofmass mode of atoms can be coupled to the vibrational mode of the membrane in free space. Via laser cooling of atoms a significant sympathetic cooling effect on the membrane vibrations can be achieved. Switching off laser cooling brings the system close to a regime of strong coherent coupling. This setup provides a controllable segregation between the cooling and coherent dynamics regimes, and allows one to keep the membrane in a cryogenic environment and atoms at a distance in a vacuum chamber.
Optomechanical approach to cooling of small polarizable particles in a strongly pumped ring cavity
Cavity cooling of an atom works best on a cyclic optical transition in the strong coupling regime near resonance, where smallcavity photon numbers suffice for trapping and cooling. A straightforward application to the cooling of the translational motion of other polarizable particles without sharply defined twolevel transitions (such as molecules) fails as optical pumping transfers the particle into uncoupled states. An alternative operation in the faroffresonant regime generates only very slow cooling due to the reduced fieldparticle coupling. We suggest one can overcome this by using a strongly driven ring cavity operated in the sideband cooling regime. The dynamics can be mapped onto the optomechanics setup with a movable mirror and allows one to take advantage of a collectively enhanced fieldparticle coupling by large photon numbers. A linearized analytical treatment confirmed by full numerical quantum simulations predicts fast cooling despite the offresonant small singleparticlesinglephoton coupling. Even groundstate translational cooling (in the external potential) can be obtained by tuning the cavity field close to the Antistokes sideband for sufficiently high trapping frequency. Numerical simulations show quantum jumps of the particle between the lowest two trapping levels, which can be directly and continuously monitored via scattered light intensity detection.
Singleatom cavity QED and optomicromechanics
M. Wallquist, K. Hammerer, P. Zoller, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, J. Ye, H. J. Kimble
In a recent publication [ 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)] we have shown the possibility to achieve strong coupling of the quantized motion of a micronsized mechanical system to the motion of a single trapped atom. In the proposed setup the coherent coupling between a SiN membrane and a single atom is mediated by the field of a high finesse cavity and can be much larger than the relevant decoherence rates. This makes the welldeveloped tools of cavity quantum electrodynamics with single atoms available in the realm of cavity optomechanics. In this article we elaborate on this scheme and provide detailed derivations and technical comments. Moreover, we give numerical as well as analytical results for a number of possible applications for transfer of squeezed or Fock states from atom to membrane as well as entanglement generation, taking full account of dissipation. In the limit of strongcoupling the preparation and verification of nonclassical states of a mesoscopic mechanical system is within reach.
Phasenoise induced limitations on cooling and coherent evolution in
optomechanical systems
We present a detailed theoretical discussion of the effects of ubiquitous laser noise on cooling and the coherent dynamics in optomechanical systems. Phase fluctuations of the driving laser induce modulations of the linearized optomechanical coupling as well as a fluctuating force on the mirror due to variations of the mean cavity intensity. We first evaluate the influence of both effects on cavity cooling and find that for a small laser linewidth, the dominant heating mechanism arises from intensity fluctuations. The resulting limit on the final occupation number scales linearly with the cavity intensity both under weak and strongcoupling conditions. For the strongcoupling regime, we also determine the effect of phase noise on the coherent transfer of single excitations between the cavity and the mechanical resonator and obtain a similar conclusion. Our results show that conditions for optical groundstate cooling and coherent operations are experimentally feasible and thus laser phase noise does pose a challenge but not a stringent limitation for optomechanical systems.
Micromechanical oscillator groundstate cooling via resonant intracavity optical gain or absorption
We suggest possibilities for manipulation and groundstate cooling of micromechanical oscillators by resonant coupling of the mirror vibrations to narrow optical transitions of a designed material ensemble within a cavity mode. Particles, modeled as a twolevel ensemble, create intracavity narrow bandwidth loss or gain and induce tailored asymmetric structuring of the cavity noise spectrum interacting with the oscillator. This facilitates cooling via inhibition of the Stokesscattering process or enhancement of antiStokes scattering even for short lowfinesse optical cavities.
Strong Coupling of a Mechanical Oscillator and a Single Atom
K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, H. J. Kimble
Physical Review Letters
103(6)
063005
(2009)

Journal

PDF
We propose and analyze a setup to achieve strong coupling between a single trapped atom and a mechanical oscillator. The interaction between the motion of the atom and the mechanical oscillator is mediated by a quantized light field in a laser driven highfinesse cavity. In particular, we show that high fidelity transfer of quantum states between the atom and the mechanical oscillator is in reach for existing or near future experimental parameters. Our setup provides the basic toolbox from atomic physics for coherent manipulation, preparation, and measurement of micromechanical and nanomechanical oscillators.
Cavityassisted squeezing of a mechanical oscillator
K. Jaehne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, P. Zoller
We investigate the creation of squeezed states of a vibrating membrane or a movable mirror in an optomechanical system. An optical cavity is driven by the squeezed light and couples via the radiation pressure to the membrane or mirror, effectively providing a squeezed heat bath for the mechanical oscillator. Under the conditions of laser cooling to the ground state, we find an efficient transfer of squeezing with roughly 60% of light squeezing conveyed to the membrane or mirror (on a dB scale). We determine the requirements on the carrier frequency and the bandwidth of squeezed light. Beyond the conditions of groundstate cooling, we predict mechanical squashing to be observable in current systems.
SubPlanckscale structures in a vibrating molecule in the presence of decoherence
Suranjana Ghosh, Utpal Roy, Claudiu Genes, David Vitali
We study the effect of decoherence on the subPlanck scale structures of the vibrational wave packet of a molecule. The time evolution of these wave packets is investigated under the influence of a photonic or phononic environment. We determine the master equation describing the reduced dynamics of the wave packet and analyze the sensitivity of the subPlanck structures against decoherence in the case of a hydrogen iodide (HI) molecule.
Quantum Effects in Optomechanical Systems
C. Genes, A. Mari, D. Vitali, P. Tombesi
Advances In Atomic Molecular and Optical Physics
57
(2009)

Book Chapter
The search for experimental demonstration of the quantum behavior of macroscopic mechanical resonators is a fast growing field of investigation and recent results suggest that the generation of quantum states of resonators with a mass at the microgram scale is within reach. In this chapter we give an overview of two important topics within this research field: cooling to the motional ground state and the generation of entanglement involving mechanical, optical, and atomic degrees of freedom. We focus on optomechanical systems where the resonator is coupled to one or more driven cavity modes by the radiationpressure interaction. We show that robust stationary entanglement between the mechanical resonator and the output fields of the cavity can be generated, and that this entanglement can be transferred to atomic ensembles placed within the cavity. These results show that optomechanical devices are interesting candidates for the realization of quantum memories and interfaces for continuous variable quantumcommunication networks.
Simultaneous cooling and entanglement of mechanical modes of a micromirror in an optical cavity
Laser cooling of a mechanical mode of a resonator by the radiation pressure of a detuned optical cavity mode has been recently demonstrated by various groups in different experimental configurations. Here, we consider the effect of a second mechanical mode with a close but different resonance frequency. We show that the nearby mechanical resonance is simultaneously cooled by the cavity field, provided that the difference between the two mechanical frequencies is not too small. When this frequency difference becomes smaller than the effective mechanical damping of the secondary mode, the two cooling processes interfere destructively similarly to what happens in electromagnetically induced transparency, and cavity cooling is suppressed in the limit of identical mechanical frequencies. We show that also the entanglement properties of the steady state of the tripartite system crucially depend upon the difference between the two mechanical frequencies. If the latter is larger than the effective damping of the second mechanical mode, the state shows fully tripartite entanglement and each mechanical mode is entangled with the cavity mode. If instead, the frequency difference is smaller, the steady state is a twomode biseparable state, inseparable only when one splits the cavity mode from the two mechanical modes. In this latter case, the entanglement of each mechanical mode with the cavity mode is extremely fragile with respect to temperature.
Robust entanglement of a micromechanical resonator with output optical fields
We perform an analysis of the optomechanical entanglement between the experimentally detectable output field of an optical cavity and a vibrating cavity endmirror. We show that by a proper choice of the readout (mainly by a proper choice of detection bandwidth) one cannot only detect the already predicted intracavity entanglement but also optimize and increase it. This entanglement is explained as being generated by a scattering process owing to which strong quantum correlations between the mirror and the optical Stokes sideband are created. Alloptical entanglement between scattered sidebands is also predicted, and it is shown that the mechanical resonator and the two sideband modes form a fully tripartiteentangled system capable of providing practicable and robust solutions for continuousvariable quantumcommunication protocols.
Emergence of atomlightmirror entanglement inside an optical cavity
We propose a scheme for the realization of a hybrid, strongly quantumcorrelated system formed of an atomic ensemble surrounded by a highfinesse optical cavity with a vibrating mirror. We show that the steady state of the system shows tripartite and bipartite continuous variable entanglement in experimentally accessible parameter regimes, which is robust against temperature.
Groundstate cooling of a micromechanical oscillator: Comparing cold damping and cavityassisted cooling schemes
C. Genes, D. Vitali, P. Tombesi, S. Gigan, M. Aspelmeyer
We provide a general framework to describe cooling of a micromechanical oscillator to its quantum ground state by means of radiationpressure coupling with a driven optical cavity. We apply it to two experimentally realized schemes, backaction cooling via a detuned cavity and colddamping quantumfeedback cooling, and we determine the ultimate quantum limits of both schemes for the full parameter range of a stable cavity. While both allow one to reach the oscillator's quantum ground state, we find that backaction cooling is more efficient in the good cavity limit, i.e., when the cavity bandwidth is smaller than the mechanical frequency, while cold damping is more suitable for the bad cavity limit. The results of previous treatments are recovered as limiting cases of specific parameter regimes.
Selfcooling of a movable mirror to the ground state using radiation pressure
We show that one can cool a micromechanical oscillator to its quantum ground state using radiation pressure in an appropriately detuned cavity (selfcooling). From a theory based on HeisenbergLangevin equations we find that optimal selfcooling occurs in the good cavity regime, when the cavity bandwidth is smaller than the mechanical frequency, but still larger than the effective mechanical damping. In this case the intracavity field and the vibrational mechanical mode coherently exchange their fluctuations, thus reducing the mirror temperature by several orders of magnitude. We also present dynamical calculations which show how to access the mirror temperature from a homodyne measurement of the fluctuations of the reflected field.
Atomic entanglement generation with reduced decoherence via fourwave mixing
In most proposals for the generation of entanglement in large ensembles of atoms via projective measurements, the interaction with the vacuum is responsible for both the generation of the signal that is detected and the spin depolarization or decoherence. In consequence, one must usually work in a regime where the information acquisition via detection is sufficiently slow (weak measurement regime) such as not to strongly disturb the system. We propose here a fourwave mixing scheme where, owing to the pumping of the atomic system into a dark state, the polarization of the ensemble is not critically affected by spontaneous emission. In the language of spin squeezing, the removal of the limitations imposed by spontaneous emission allows one to work in a strong signal regime where the Heisenberg limit can be reached.
Cooperative spin decoherence and population transfer
An ensemble of multilevel atoms is a good candidate for a quantum information storage device. The information is encrypted in the collective ground state atomic coherence, which, in the absence of external excitation, is decoupled from the vacuum and therefore decoherence free. However, in the process of manipulation of atoms with light pulses (writing, reading), one inadvertently introduces a coupling to the environment, i.e., a source of decoherence. The dissipation process is often treated as an independent process for each atom in the ensemble, an approach which fails at large atomic optical depths where cooperative effects must be taken into account. In this paper, the cooperative behavior of spin decoherence and population transfer for a system of two, driven multilevel atoms is studied. Not surprisingly, an enhancement in the decoherence rate is found, when the atoms are separated by a distance that is small compared to an optical wavelength; however, it is found that this rate increases even further for somewhat larger separations for atoms aligned along the direction of the driving field's propagation vector. A treatment of the cooperative modification of optical pumping rates and an effect of polarization swapping between atoms is also discussed, lending additional insight into the origin of the collective decay.
Generating conditional atomic entanglement by measuring photon number in a single output channel
The polarization analysis of quantized probe light transmitted through an atomic ensemble has been used to prepare entangled collective atomic states. In a "balanced" detection configuration, where the difference signal from two detection ports is analyzed, the continuous monitoring of a component of the Stokes field vector provides a means for conditional projective measurements on the atomic system. Here, we make use of classical driving fields, in the pulsed regime, and of an "unbalanced" detection setup (single detector) where the effective photon number of scattered photons is the detected observable. Conditional atomic spin squeezed states and superpositions of such squeezed states can be prepared in this manner.
Spin squeezing via atomfield interactions is considered within the context of the TavisCummings model. An ensemble of N twolevel atoms interacts with a quantized cavity field. For all the atoms initially in their ground states, it is shown that spin squeezing of both the atoms and the field can be achieved provided the initial state of the cavity field has coherence between number states differing by 2. Most of the discussion is restricted to the case of a cavity field initially in a coherent state, but initial squeezed states for the field are also discussed. Optimal conditions for obtaining squeezing are obtained. An analytic solution is found that is valid in the limit that the number of atoms is much greater than unity and is also much larger than the average number of photons, alpha(2), initially in the coherent state of the cavity field. In this limit, the degree of spin squeezing increases with increasing a, even though the field more closely resembles a classical field for which no spin squeezing could be achieved.