Superradiant rayleigh scattering and collective atomic recoil lasing in a ring cavity

Universality of Dicke superradiance in arrays of quantum emitters

Dicke superradiance is an example of emergence of macroscopic quantum coherence via correlated dissipation. Starting from an initially incoherent state, a collection of excited atoms synchronizes as they decay, generating a macroscopic dipole moment and emitting a short and intense pulse of light. While well understood in cavities, superradiance remains an open problem in extended systems due to the exponential growth of complexity with atom number. Here we show that Dicke superradiance is a universal phenomenon in ordered arrays. We present a theoretical framework – which circumvents the exponential complexity of the problem – that allows us to predict the critical distance beyond which Dicke superradiance disappears. This critical distance is highly dependent on the dimensionality and atom number. Our predictions can be tested in state of the art experiments with arrays of neutral atoms, molecules, and solid-state emitters and pave the way towards understanding the role of many-body decay in quantum simulation, metrology, and lasing.

Dicke superradiance is an important collective quantum phenomenon, but its analysis is hindered by the exponential growth of the state space with atom number. Here, the authors develop a theoretical framework that overcomes this, and predict a critical distance below which superradiant decay can be observed in large ordered arrays.

Momentum Halo in The Rayleigh Scattering by a Bose–Einstein Condensate

A ring of radius ℏk0 in the momentum distribution of a Bose–Einstein condensate is visible when the atoms scatter a single photon. Here, we describe an approximated theory of this effect, leading to an analytic expression of the isotropic momentum scattering rate.

Vibration damping platform for cavity quantum-electrodynamics experiments

We present a mechanical platform with enhanced vibration damping properties for cavity quantum-electrodynamics experiments. It is based on a composite design that combines a soft, vibration damping core with a rigid shell maintaining optical alignment. It passively damps the vibrations generated by piezoelectric actuators controlling the mirror positions. The mechanical resonances of the platform, which lead to a length change of the cavity, are efficiently suppressed up to 100 kHz. Our platform is ultra-high vacuum compatible and can be used in most applications, in particular, where long cavities and optical access to the cavity center are required.

Classical and Quantum Collective Recoil Lasing: A Tutorial

Collective atomic recoil lasing (CARL) is a process during which an ensemble of cold atoms, driven by a far-detuned laser beam, spontaneously organize themselves in periodic structures on the scale of the optical wavelength. The principle was envisaged by R. Bonifacio in 1994 and, ten years later, observed in a series of experiments in Tübingen by C. Zimmermann and colleagues. Here, we review the basic model of CARL in the classical and in the quantum regime.

Multimode Collective Atomic Recoil Lasing in Free Space

Cold atomic clouds in collective atomic recoil lasing are usually confined by an optical cavity, which forces the light-scattering to befall in the mode fixed by the resonator. Here we consider the system to be in free space, which leads into a vacuum multimode collective scattering. We show that the presence of an optical cavity is not always necessary to achieve coherent collective emission by the atomic ensemble and that a preferred scattering path arises along the major axis of the atomic cloud. We derive a full vectorial model for multimode collective atomic recoil lasing in free space. Such a model consists of multi-particle equations capable of describing the motion of each atom in a 2D/3D cloud. These equations are numerically solved by means of molecular dynamic algorithms, usually employed in other scientific fields. The numerical results show that both atomic density and collective scattering patterns are applicable to the cloud’s orientation and shape and to the polarization of the incident light.

Strongly correlated Fermions strongly coupled to light

Strong quantum correlations in matter are responsible for some of the most extraordinary properties of materials, from magnetism to high-temperature superconductivity, but their integration in quantum devices requires a strong, coherent coupling with photons, which still represents a formidable technical challenge in solid state systems. In cavity quantum electrodynamics, quantum gases such as Bose-Einstein condensates or lattice gases have been strongly coupled with light. However, neither Fermionic quantum matter, comparable to electrons in solids, nor atomic systems with controlled interactions, have thus far been strongly coupled with photons. Here we report on the strong coupling of a quantum-degenerate unitary Fermi gas with light in a high finesse cavity. We map out the spectrum of the coupled system and observe well resolved dressed states, resulting from the strong coupling of cavity photons with each spin component of the gas. We investigate spin-balanced and spin-polarized gases and find quantitative agreement with ab initio calculation describing light-matter interaction. Our system offers complete and simultaneous control of atom-atom and atom-photon interactions in the quantum degenerate regime, opening a wide range of perspectives for quantum simulation.

Extended Bose-Hubbard Model with Cavity-Mediated Infinite-Range Interactions at Finite Temperatures

We consider the finite-temperature properties of the extended Bose-Hubbard model realized recently in an ETH experiment [Nature 532, 476 (2016)]. Competing short- and global-range interactions accommodate fascinating collective phenomena. We formulate a self-consistent mean-field theory to describe the behaviors of the system at finite temperatures. At a fixed chemical potential, we map out the distributions of the superfluid order parameters and number densities with respect to the temperatures. For a charge density wave, we find that the global-range interaction enhances the charge order by increasing the transition temperature at which the charge order melts out, while for a supersolid phase, we find that the disappearance of the charge order and the superfluid order occurs at different temperature. At a fixed number-density filling factor, we extract the temperature dependence of the thermodynamic functions such as internal energy, specific heat and entropy. Across the superfluid phase transition, the specific heat has a discontinuous jump.

Supersolid Properties of a Bose-Einstein Condensate in a Ring Resonator

We investigate the dynamics of a Bose-Einstein condensate interacting with two noninterfering and counterpropagating modes of a ring resonator. Superfluid, supersolid, and dynamic phases are identified experimentally and theoretically. The supersolid phase is obtained for sufficiently equal pump strengths for the two modes. In this regime we observe the emergence of a steady state with crystalline order, which spontaneously breaks the continuous translational symmetry of the system. The supersolidity of this state is demonstrated by the conservation of global phase coherence at the superfluid to supersolid phase transition. Above a critical pump asymmetry the system evolves into a dynamic runaway instability commonly known as collective atomic recoil lasing. We present a phase diagram and characterize the individual phases by comparing theoretical predictions with experimental observations.

Pulse Delay Time Statistics in a Superradiant Laser with Calcium Atoms

Cold samples of calcium atoms are prepared in the metastable ^{3}P_{1} state inside an optical cavity resonant with the narrow band (375 Hz) ^{1}S_{0}→^{3}P_{1} intercombination line at 657 nm. We observe a superradiant emission of hyperbolic secant shaped pulses into the cavity with an intensity proportional to the square of the atom number, a duration much shorter than the natural lifetime of the ^{3}P_{1} state, and a delay time fluctuating from shot to shot in excellent agreement with theoretical predictions. Our incoherent pumping scheme to produce inversion on the ^{1}S_{0}→^{3}P_{1} transition should be extendable to allow for continuous wave laser operation.

Dynamical Phase Transitions to Optomechanical Superradiance

We theoretically analyze superradiant emission of light from an ultracold gas of bosonic atoms confined in a bad cavity. A metastable dipolar transition of the atoms couples to the cavity field and is incoherently pumped, and the mechanical effects of cavity-atom interactions tend to order the atoms in the periodic cavity potential. By means of a mean-field model we determine the conditions on the cavity parameters and pump rate that lead to the buildup of a stable macroscopic dipole emitting coherent light. We show that this occurs when the superradiant decay rate and the pump rate exceed threshold values of the order of the photon recoil energy. Above these thresholds superradiant emission is accompanied by the formation of stable matter-wave gratings that diffract the emitted photons. Outside of this regime, instead, the optomechanical coupling can give rise to dephasing or chaos, for which the emitted light is respectively incoherent or chaotic. These behaviors exhibit the features of a dynamical phase transitions and emerge from the interplay between global optomechanical interactions, quantum fluctuations, and noise.

Supersolid-Based Gravimeter in a Ring Cavity

We propose a novel type of composite light-matter interferometer based on a supersolidlike phase of a driven Bose-Einstein condensate coupled to a pair of degenerate counterpropagating electromagnetic modes of an optical ring cavity. The supersolidlike condensate under the influence of the gravity drags the cavity optical potential with itself, thereby changing the relative phase of the two cavity electromagnetic fields. Monitoring the phase evolution of the cavity output fields thus allows for a nondestructive measurement of the gravitational acceleration. We show that the sensitivity of the proposed gravimeter exhibits Heisenberg-like scaling with respect to the atom number. As the relative phase of the cavity fields is insensitive to photon losses, the gravimeter is robust against these deleterious effects. For state-of-the-art experimental parameters, the relative sensitivity Δg/g of such a gravimeter could be of the order of 10^{-10}-10^{-8} for a condensate of a half a million atoms and interrogation time of the order of a few seconds.

Pinning Transition of Bose-Einstein Condensates in Optical Ring Resonators

We experimentally investigate the dynamic instability of Bose-Einstein condensates in an optical ring resonator that is asymmetrically pumped in both directions. We find that, beyond a critical resonator-pump detuning, the system becomes stable regardless of the pump strength. Phase diagrams and quenching curves are presented and described by numerical simulations. We discuss a physical explanation based on a geometric interpretation of the underlying nonlinear equations of motion.

Violent relaxation in quantum fluids with long-range interactions

Violent relaxation is a process that occurs in systems with long-range interactions. It has the peculiar feature of dramatically amplifying small perturbations, and rather than driving the system to equilibrium, it instead leads to slowly evolving configurations known as quasistationary states that fall outside the standard paradigm of statistical mechanics. Violent relaxation was originally identified in gravity-driven stellar dynamics; here, we extend the theory into the quantum regime by developing a quantum version of the Hamiltonian mean field (HMF) model which exemplifies many of the generic properties of long-range interacting systems. The HMF model can either be viewed as describing particles interacting via a cosine potential, or equivalently as the kinetic XY model with infinite-range interactions, and its quantum fluid dynamics can be obtained from a generalized Gross-Pitaevskii equation. We show that singular caustics that form during violent relaxation are regulated by interference effects in a universal way described by Thom's catastrophe theory applied to waves and this leads to emergent length scales and timescales not present in the classical problem. In the deep quantum regime we find that violent relaxation is suppressed altogether by quantum zero-point motion. Our results are relevant to laboratory studies of self-organization in cold atomic gases with long-range interactions.

Self-Adapted Floquet Dynamics of Ultracold Bosons in a Cavity

Floquet dynamics of a quantum system subject to periodic modulations of system parameters provides a powerful tool for engineering new quantum matter with exotic properties. While system dynamics is significantly altered, the periodic modulation itself is usually induced externally and independent of Floquet dynamics. Here we propose a new type of Floquet physics for a Bose-Einstein condensate (BEC) subject to a shaken lattice generated inside a cavity, where the shaken lattice and atomic Floquet bands are mutually dependent, resulting in self-adapted Floquet dynamics. In particular, the shaken lattice induces Floquet quasienergy bands for the BEC, whose backaction leads to a self-adapted dynamical normal-superradiant phase transition for the shaken lattice. Such self-adapted Floquet dynamics shows two surprising and unique features: (i) The normal-superradiant phase transition possesses a hysteresis even without atom interactions. (ii) The dynamical atom-cavity steady state could exist at free energy maxima. The atom interactions strongly affect the phase transition of the BEC from zero to finite momenta. Our results provide a powerful platform for exploring self-adapted Floquet physics, which may open an avenue for engineering novel quantum materials.

Lasing by driven atoms-cavity system in collective strong coupling regime

The interaction of laser cooled atoms with resonant light is determined by the natural linewidth of the excited state. An optical cavity is another optically resonant system where the loss from the cavity determines the resonant optical response of the system. The near resonant combination of an optical Fabry-Pérot cavity with laser cooled and trapped atoms couples two distinct optical resonators via light and has great potential for precision measurements and the creation of versatile quantum optics systems. Here we show how driven magneto-optically trapped atoms in collective strong coupling regime with the cavity leads to lasing at a frequency red detuned from the atomic transition. Lasing is demonstrated experimentally by the observation of a lasing threshold accompanied by polarization and spatial mode purity, and line-narrowing in the outcoupled light. Spontaneous emission into the cavity mode by the driven atoms stimulates lasing action, which is capable of operating as a continuous wave laser in steady state, without a seed laser. The system is modeled theoretically, and qualitative agreement with experimentally observed lasing is seen. Our result opens up a range of new measurement possibilities with this system.

Disorder-Driven Density and Spin Self-Ordering of a Bose-Einstein Condensate in a Cavity

We study spatial spin and density self-ordering of a two-component Bose-Einstein condensate via collective Raman scattering into a linear cavity mode. The onset of the Dicke superradiance phase transition is marked by a simultaneous appearance of a crystalline density order and a spin-wave order. The latter spontaneously breaks the discrete Z_{2} symmetry between even and odd sites of the cavity optical potential. Moreover, in the superradiant state the continuous U(1) symmetry of the relative phase of the two condensate wave functions is explicitly broken by the cavity-induced position-dependent Raman coupling with a zero spatial average. Thus, the spatially averaged relative condensate phase is locked at either π/2 or -π/2. This continuous symmetry breaking and relative condensate phase locking by a zero-average Raman field can be considered as a generic order-by-disorder process similar to the random-field-induced order in the two-dimensional classical ferromagnetic XY spin model. However, the seed of the random field in our model stems from quantum fluctuations in the cavity field and is a dynamical entity affected by self-ordering. The spectra of elementary excitations exhibit the typical mode softening at the superradiance threshold.

Superradiant Topological Peierls Insulator inside an Optical Cavity

We consider a spinless ultracold Fermi gas tightly trapped along the axis of an optical resonator and transversely illuminated by a laser closely tuned to a resonator mode. At a certain threshold pump intensity, the homogeneous gas density breaks a Z_{2} symmetry towards a spatially periodic order, which collectively scatters pump photons into the cavity. We show that this known self-ordering transition also occurs for low field seeking fermionic particles when the laser light is blue detuned to an atomic transition. The emergent superradiant optical lattice in this case is homopolar and possesses two distinct dimerizations. Depending on the spontaneously chosen dimerization, the resulting Bloch bands can have a nontrivial topological structure characterized by a nonvanishing Zak phase. In the case where the Fermi momentum is close to half of the cavity-mode wave number, a Peierls-like instability here creates a topological insulator with a gap at the Fermi surface, which hosts a pair of edge states. The topological features of the system can be nondestructively observed via the cavity output: the Zak phase of the bulk coincides with the relative phase between laser and cavity field, while the fingerprint of edge states can be observed as additional broadening in a well-defined frequency window of the cavity spectrum.

Cavity-Assisted Measurement and Coherent Control of Collective Atomic Spin Oscillators

We demonstrate continuous measurement and coherent control of the collective spin of an atomic ensemble undergoing Larmor precession in a high-finesse optical cavity. The coupling of the precessing spin to the cavity field yields phenomena similar to those observed in cavity optomechanics, including cavity amplification, damping, and optical spring shifts. These effects arise from autonomous optical feedback onto the atomic spin dynamics, conditioned by the cavity spectrum. We use this feedback to stabilize the spin in either its high- or low-energy state, where, in equilibrium with measurement backaction heating, it achieves a steady-state temperature, indicated by an asymmetry between the Stokes and the anti-Stokes scattering rates. For sufficiently large Larmor frequency, such feedback stabilizes the spin ensemble in a nearly pure quantum state, in spite of continuous measurement by the cavity field.

Self-Ordered Limit Cycles, Chaos, and Phase Slippage with a Superfluid inside an Optical Resonator

We study dynamical phases of a driven Bose-Einstein condensate coupled to the light field of a high-Q optical cavity. For high field seeking atoms at red detuning the system is known to show a transition from a spatially homogeneous steady state to a self-ordered regular lattice exhibiting superradiant scattering into the cavity. For blue atom pump detuning the particles are repelled from the maxima of the light-induced optical potential suppressing scattering. We show that this generates a new dynamical instability of the self-ordered phase, leading to the appearance of self-ordered stable limit cycles characterized by large amplitude self-sustained oscillations of both the condensate density and cavity field. The limit cycles evolve into chaotic behavior by period doubling. Large amplitude oscillations of the condensate are accompanied by phase slippage through soliton nucleation at a rate that increases in the chaotic regime. Different from a superfluid in a closed setup, this driven dissipative superfluid is not destroyed by the proliferation of solitons since kinetic energy is removed through cavity losses.

Synchronization of Bloch oscillations by a ring cavity

We consider Bloch oscillations of ultracold atoms stored in a one-dimensional vertical optical lattice and simultaneously interacting with a unidirectionally pumped optical ring cavity whose vertical arm is collinear with the optical lattice. We find that the feedback provided by the cavity field on the atomic motion synchronizes Bloch oscillations via a mode-locking mechanism, steering the atoms to the lowest Bloch band. It also stabilizes Bloch oscillations against noise, and even suppresses dephasing due to atom-atom interactions. Furthermore, it generates periodic bursts of light emitted into the counter-propagating cavity mode, providing a non-destructive monitor of the atomic dynamics. All these features may be crucial for future improvements of the design of atomic gravimeters based on recording Bloch oscillations.

Quantum threshold for optomechanical self-structuring in a Bose-Einstein condensate

Theoretical analysis of the optomechanics of degenerate bosonic atoms with a single feedback mirror shows that self-structuring occurs only above an input threshold that is quantum mechanical in origin. This threshold also implies a lower limit to the size (period) of patterns that can be produced in a condensate for a given pump intensity. These thresholds are interpreted as due to the quantum rigidity of Bose-Einstein condensates, which has no classical counterpart. Above the threshold, the condensate self-organizes into an ordered supersolid state with a spatial period self-selected by optical diffraction.

Cavity-modified collective Rayleigh scattering of two atoms

We report on the observation of cooperative radiation of exactly two neutral atoms strongly coupled to the single mode field of an optical cavity, which is close to the lossless-cavity limit. Monitoring the cavity output power, we observe constructive and destructive interference of collective Rayleigh scattering for certain relative distances between the two atoms. Because of cavity backaction onto the atoms, the cavity output power for the constructive two-atom case (N=2) is almost equal to the single-emitter case (N=1), which is in contrast to free-space where one would expect an N^{2} scaling of the power. These effects are quantitatively explained by a classical model as well as by a quantum mechanical model based on Dicke states. We extract information on the relative phases of the light fields at the atom positions and employ advanced cooling to reduce the jump rate between the constructive and destructive atom configurations. Thereby we improve the control over the system to a level where the implementation of two-atom entanglement schemes involving optical cavities becomes realistic.

Backaction-driven transport of Bloch oscillating atoms in ring cavities

We predict that an atomic Bose-Einstein condensate strongly coupled to an intracavity optical lattice can undergo resonant tunneling and directed transport when a constant and uniform bias force is applied. The bias force induces Bloch oscillations, causing amplitude and phase modulation of the lattice which resonantly modifies the site-to-site tunneling. For the right choice of parameters a net atomic current is generated. The transport velocity can be oriented oppositely to the bias force, with its amplitude and direction controlled by the detuning between the pump laser and the cavity. The transport can also be enhanced through imbalanced pumping of the two counterpropagating running wave cavity modes. Our results add to the cold atoms quantum simulation toolbox, with implications for quantum sensing and metrology.

Steering matter wave superradiance with an ultranarrow-band optical cavity

A superfluid atomic gas is prepared inside an optical resonator with an ultranarrow bandwidth on the order of the single photon recoil energy. When a monochromatic off-resonant laser beam irradiates the atoms, above a critical intensity the cavity emits superradiant light pulses with a duration on the order of its photon storage time. The atoms are collectively scattered into coherent superpositions of discrete momentum states, which can be precisely controlled by adjusting the cavity resonance frequency. With appropriate pulse sequences the entire atomic sample can be collectively accelerated or decelerated by multiples of two recoil momenta. The instability boundary for the onset of matter wave superradiance is recorded and its main features are explained by a mean field model.

Realization of the Dicke model using cavity-assisted Raman transitions

We realize an open version of the Dicke model by coupling two hyperfine ground states using two cavity-assisted Raman transitions. The interaction due to only one of the couplings is described by the Tavis-Cummings model and we observe a normal mode splitting in the transmission around the dispersively shifted cavity. With both couplings present the dynamics are described by the Dicke model and we measure the onset of superradiant scattering into the cavity above a critical coupling strength.

Ensemble inequivalence in systems with wave-particle interaction

The classical wave-particle Hamiltonian is considered in its generalized version, where two modes are assumed to interact with the coevolving charged particles. The equilibrium statistical mechanics solution of the model is worked out analytically, both in the canonical and the microcanonical ensembles. The competition between the two modes is shown to yield ensemble inequivalence, at variance with the standard scenario where just one wave is allowed to develop. As a consequence, both temperature jumps and negative specific heat can show up in the microcanonical ensemble. The relevance of these findings for both plasma physics and free electron laser applications is discussed.

Umklapp superradiance with a collisionless quantum degenerate Fermi gas

The quantum dynamics of the electromagnetic light mode of an optical cavity filled with a coherently driven Fermi gas of ultracold atoms strongly depends on the geometry of the Fermi surface. Superradiant light generation and self-organization of the atoms can be achieved at low pumping threshold due to resonant atom-photon umklapp processes, where the fermions are scattered from one side of the Fermi surface to the other by exchanging photon momenta. The cavity spectrum exhibits sidebands that, despite strong atom-light coupling and cavity decay, retain narrow linewidth, due to absorptionless transparency windows outside the atomic particle-hole continuum and the suppression of broadening and thermal fluctuations in the collisionless Fermi gas.

Dynamical instability of a Bose-Einstein condensate in an optical ring resonator

We experimentally investigate the dynamical instability of a Bose-Einstein condensate in an optical ring resonator for various cavity detuning and pump powers. The resulting stability diagram is asymmetric with respect to the cavity detuning and can be described by the coupling of two atomic modes with one optical mode. We compare the experimental data to a numerical simulation and to an analytic expression of the phase boundary. For positive and negative pump cavity detuning, different coupling mechanisms are identified explaining the asymmetry of the stability diagram. We present a physical interpretation and discuss the connection to the Dicke quantum phase transition.

Kinetic theory for transverse optomechanical instabilities

We investigate transverse symmetry-breaking instabilities emerging from the optomechanical coupling between light and the translational degrees of freedom of a collisionless, damping-free gas of cold, two-level atoms. We develop a kinetic theory that can also be mapped on to the case of an electron plasma under ponderomotive forces. A general criterion for the existence and spatial scale of transverse instabilities is identified; in particular, we demonstrate that monotonically decreasing velocity distribution functions are always unstable.

Recoil effects of a motional scatterer on single-photon scattering in one dimension

The scattering of a single photon with sufficiently high energy can cause a recoil of a motional scatterer. We study its backaction on the photon's coherent transport in one dimension by modeling the motional scatterer as a two-level system, which is trapped in a harmonic potential. While the reflection spectrum is of a single peak in the Lamb-Dicke limit, multi-peaks due to phonon excitations can be observed in the reflection spectrum as the trap becomes looser or the mass of the two-level system becomes smaller.

Cavity Cooling Below the Recoil Limit

Conventional laser cooling relies on repeated electronic excitations by near-resonant light, which constrains its area of application to a selected number of atomic species prepared at moderate particle densities. Optical cavities with sufficiently large Purcell factors allow for laser cooling schemes, avoiding these limitations. Here, we report on an atom-cavity system, combining a Purcell factor above 40 with a cavity bandwidth below the recoil frequency associated with the kinetic energy transfer in a single photon scattering event. This lets us access a yet-unexplored regime of atom-cavity interactions, in which the atomic motion can be manipulated by targeted dissipation with sub-recoil resolution. We demonstrate cavity-induced heating of a Bose-Einstein condensate and subsequent cooling at particle densities and temperatures incompatible with conventional laser cooling.

Role reversal in a Bose-condensed optomechanical system

We analyze the optomechanicslike properties of a Bose-Einstein condensate (BEC) trapped inside an optical resonator and driven by both a classical and a quantized light field. We find that this system exhibits the nature of role reversal between the matter-wave field and the quantized light field. As a result, the matter-wave field now plays the role of the quantized light field, and the quantized light field behaves like a movable mirror, in contrast to the familiar situation in BEC-based cavity optomechanics [Brennecke et al., Science 322, 235 (2008); Murch et al., Nature Phys. 4, 561 (2008)]. We demonstrate that this system can lead to the creation of a variety of nonclassical matter-wave fields, in particular, cat states, and discuss several possible protocols to measure their Wigner function.

Rapid coherent optical modulation of atomic momenta via pseudoresonances

We show that modulation of an optical field injected into a cavity containing a dilute Bose-Einstein condensate is transformed into a modulation of the population of the atomic momentum states due to pseudoresonances of the resolvent which describes the linearized evolution of the atom-cavity system. This effect is related to the way the atomic momentum states and the cavity optical field are dynamically coupled. The results presented offer new possibilities for rapid modulation of atomic momentum state populations up to 3 orders of magnitude faster than modulation of magnetic trapping potentials.

Fast cavity-enhanced atom detection with low noise and high fidelity

Cavity quantum electrodynamics describes the fundamental interactions between light and matter, and how they can be controlled by shaping the local environment. For example, optical microcavities allow high-efficiency detection and manipulation of single atoms. In this regime, fluctuations of atom number are on the order of the mean number, which can lead to signal fluctuations in excess of the noise on the incident probe field. Here we demonstrate, however, that nonlinearities and multi-atom statistics can together serve to suppress the effects of atomic fluctuations when making local density measurements on clouds of cold atoms. We measure atom densities below 1 per cavity mode volume near the photon shot-noise limit. This is in direct contrast to previous experiments where fluctuations in atom number contribute significantly to the noise. Atom detection is shown to be fast and efficient, reaching fidelities in excess of 97% after 10 μs and 99.9% after 30 μs.

Single atoms can be detected using optical resonators that extend the lifetime of the photon. Here, the authors demonstrate fast, high-fidelity detection of very low atom densities using a microfabricated optical cavity to couple the detection light with the atoms.

Cavity-controlled collective scattering at the recoil limit

We study collective scattering with Bose-Einstein condensates interacting with a high-finesse ring cavity. The condensate scatters the light of a transverse pump beam superradiantly into modes which, in contrast to previous experiments, are not determined by the geometrical shape of the condensate, but specified by a resonant cavity mode. Moreover, since the recoil-shifted frequency of the scattered light depends on the initial momentum of the scattered fraction of the condensate, we show that it is possible to employ the good resolution of the cavity as a filter selecting particular quantized momentum states.

In situ characterization of an optical cavity using atomic light shift

We report the precise characterization of the optical potential obtained by injecting a distributed-feedback erbium-doped fiber laser at 1560 nm to the transverse modes of a folded optical cavity. The optical potential was mapped in situ using cold rubidium atoms, whose potential energy was spectrally resolved thanks to the strong differential light shift induced by the 1560 nm laser on the two levels of the probe transition. The optical potential obtained in the cavity is suitable for trapping rubidium atoms and eventually to achieve all-optical Bose-Einstein condensation directly in the resonator.

Multi-normal mode-splitting for an optical cavity with electromagnetically induced transparency medium

We theoretically study the cavity transmission spectra with three-level atoms coupled by a coherent external control field in the superstrong coupling regime (atoms-cavity coupling strength g [square root] N is near or larger than the cavity free-spectral range DeltaFSR). When satisfying the superstrong coupling condition by increasing the number of the interaction atoms, more than one FSR cavity modes interact with atoms and each mode will split three peaks, which can be well explained by the linear dispersion enhancement of electromagnetically induced transparency medium due to the largely increased atomic density in the cavity.

Electromagnetic wave dynamics in matter-wave superradiant scattering

We present a small-signal wave propagation theory on matter-wave superradiant scattering. We show, in a longitudinally excited condensate, that the backward-propagating, superradiantly generated optical field propagates with ultraslow group velocity and that the small-signal gain profile has a Bragg resonance. We further show a unidirectional suppression of optical superradiant scattering, and explain why matter-wave superradiance can occur only when the pump laser is red detuned. This is the first analytical theory on field propagation in matter-wave superradiance that can explain all matter-wave superradiance experiments to date that used a single-frequency, long-pulse, red-detuned laser.

Cavity-mediated strong matter wave bistability in a spin-1 condensate

We study matter-wave bistability in a spin-1 Bose-Einstein condensate dispersively coupled to a unidirectional ring cavity. A unique feature is that the population exchange among different modes of matter fields is accomplished via spin-exchange collisions. We show that the interplay between the atomic spin mixing and the cavity light field can lead to a strong matter-wave nonlinearity, making matter-wave bistability in a cavity at the single-photon level achievable.

Strong magnetic coupling of an ultracold gas to a superconducting waveguide cavity

Placing an ensemble of 10;{6} ultracold atoms in the near field of a superconducting coplanar waveguide resonator with a quality factor Q approximately 10;{6}, one can achieve strong coupling between a single microwave photon in the coplanar waveguide resonator and a collective hyperfine qubit state in the ensemble with g_{eff}/2pi approximately 40 kHz larger than the cavity linewidth of kappa/2pi approximately 7 kHz. Integrated on an atomchip, such a system constitutes a hybrid quantum device, which also can be used to interconnect solid-state and atomic qubits, study and control atomic motion via the microwave field, observe microwave superradiance, build an integrated micromaser, or even cool the resonator field via the atoms.

Excess noise depletion of a Bose-Einstein condensate in an optical cavity

Quantum fluctuations of a cavity field coupled into the motion of ultracold bosons can be strongly amplified by a mechanism analogous to the Petermann excess noise factor in lasers with unstable cavities. For a Bose-Einstein condensate in a stable optical resonator, the excess noise effect amounts to a significant depletion on long time scales.

Quantum nondemolition measurements and state preparation in quantum gases by light detection

We consider light scattering from ultracold quantum gas in optical lattices into a cavity. The measurement of photons leaking out of the cavity enables a quantum nondemolition access to various atomic variables. The time resolved light detection projects the motional state to various atom-number squeezed and macroscopic superposition states that strongly depend on the geometry. Modifications of the atomic and light properties at a single quantum trajectory are demonstrated. The quantum structure of final states can be revealed by further observations of the same sample.

Dynamical bottlenecks to intramolecular energy flow

Vibrational energy flows unevenly in molecules, repeatedly going back and forth between trapping and roaming. We identify bottlenecks between diffusive and chaotic behavior, and describe generic mechanisms of these transitions, taking the carbonyl sulfide molecule OCS as a case study. The bottlenecks are found to be lower-dimensional tori; their bifurcations and unstable manifolds govern the transition mechanisms.

Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip

An optical cavity enhances the interaction between atoms and light, and the rate of coherent atom-photon coupling can be made larger than all decoherence rates of the system. For single atoms, this 'strong coupling regime' of cavity quantum electrodynamics has been the subject of many experimental advances. Efforts have been made to control the coupling rate by trapping the atom and cooling it towards the motional ground state; the latter has been achieved in one dimension so far. For systems of many atoms, the three-dimensional ground state of motion is routinely achieved in atomic Bose-Einstein condensates (BECs). Although experiments combining BECs and optical cavities have been reported recently, coupling BECs to cavities that are in the strong-coupling regime for single atoms has remained an elusive goal. Here we report such an experiment, made possible by combining a fibre-based cavity with atom-chip technology. This enables single-atom cavity quantum electrodynamics experiments with a simplified set-up and realizes the situation of many atoms in a cavity, each of which is identically and strongly coupled to the cavity mode. Moreover, the BEC can be positioned deterministically anywhere within the cavity and localized entirely within a single antinode of the standing-wave cavity field; we demonstrate that this gives rise to a controlled, tunable coupling rate. We study the heating rate caused by a cavity transmission measurement as a function of the coupling rate and find no measurable heating for strongly coupled BECs. The spectrum of the coupled atoms-cavity system, which we map out over a wide range of atom numbers and cavity-atom detunings, shows vacuum Rabi splittings exceeding 20 gigahertz, as well as an unpredicted additional splitting, which we attribute to the atomic hyperfine structure. We anticipate that the system will be suitable as a light-matter quantum interface for quantum information.

Cavity QED with a Bose-Einstein condensate

Cavity quantum electrodynamics (cavity QED) describes the coherent interaction between matter and an electromagnetic field confined within a resonator structure, and is providing a useful platform for developing concepts in quantum information processing. By using high-quality resonators, a strong coupling regime can be reached experimentally in which atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in. This has led to fundamental studies with both microwave and optical resonators. To meet the challenges posed by quantum state engineering and quantum information processing, recent experiments have focused on laser cooling and trapping of atoms inside an optical cavity. However, the tremendous degree of control over atomic gases achieved with Bose-Einstein condensation has so far not been used for cavity QED. Here we achieve the strong coupling of a Bose-Einstein condensate to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This is a conceptually new regime of cavity QED, in which all atoms occupy a single mode of a matter-wave field and couple identically to the light field, sharing a single excitation. This opens possibilities ranging from quantum communication to a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions.