We demonstrate optical nonlinearities due to the interaction of weak optical fields with the collective motion of a strongly dispersive ultracold gas. The combination of a recoil-induced resonance (RIR) in the high gain regime and optical waveguiding within the dispersive medium enables us to achieve a collective atomic cooperativity of $275 \pm 50$ even in the absence of a cavity. As a result, we observe optical bistability at input powers as low as 20 pW. The present scheme allows for dynamic optical control of the dispersive properties of the ultracold gas using very weak pulses of light. The experimental observations are in good agreement with a theoretical model.
We study the collective motion of atoms confined in an optical lattice operating inside a high finesse ring cavity. A simplified theoretical model for the dynamics of the system is developed upon the assumption of adiabaticity of the atomic motion. We show that in a regime where the light shift per photon times the number of atoms exceeds the line width of the cavity resonance, the otherwise tiny retro-action of the atoms upon the light field becomes a significant feature of the system, giving rise to dispersive optical bistability of the intra-cavity field. A solution of the complete set of c…
The recoil of atoms in arrays due to the emission or absorption of photons is studied for sub-wavelength interatomic spacing. The atoms in the array interact with each other through collective dipole-dipole interactions and with the incident laser field in the low intensity limit. Shining uniform light on the array gives rise to patterns of excitation and recoil in the array. These arise due to the interference of different eigenmodes of excitation. The relation between the recoil and the decay dynamics is studied when the array is in its excitation eigenstates. The recoil experienced by a sub…
Self-organization effects related to light amplification in the collective atomic recoil laser system with the driven atoms confined in a harmonic trap are investigated further. In the dispersive parametric region, our study reveals that the spontaneously formed structures in the phase space contributes an important role to the light amplification of the probe field under the atomic motion being modified by the trap.
We observe the buildup of a frequency-shifted reverse light field in a unidirectionally pumped high-$Q$ optical ring cavity serving as a dipole trap for cold atoms. This effect is enhanced and a steady state is reached, if via an optical molasses an additional friction force is applied to the atoms. We observe the displacement of the atoms accelerated by momentum transfer in the backscattering process and interpret our observations in terms of the collective atomic recoil laser. Numerical simulations are in good agreement with the experimental results.
We formulate a wave atom optics theory of the Collective Atomic Recoil Laser, where the atomic center-of-mass motion is treated quantum mechanically. By comparing the predictions of this theory with those of the ray atom optics theory, which treats the center-of-mass motion classically, we show that for the case of a far off-resonant pump laser the ray optics model fails to predict the linear response of the CARL when the temperature is of the order of the recoil temperature or less. This is due to the fact that in theis temperature regime one can no longer ignore the effects of matter-wave di…
We extend the Collective Atomic Recoil Lasing (CARL) model including the effects of friction and diffusion forces acting on the atoms due to the presence of optical molasses fields. The results from this model are consistent with those from a recent experiment by Kruse et al. [Phys. Rev. Lett. 91, 183601 (2003)]. In particular, we obtain a threshold condition above which collective backscattering occurs. Using a nonlinear analysis we show that the backscattered field and the bunching evolve to a steady-state, in contrast to the non-stationary behaviour of the standard CARL model. For a proper …
We report on Kerr nonlinearity and dispersive optical bistability of a Fabry-Perot optical resonator due to the displacement of ultracold atoms trapped within. In the driven resonator, such collective motion is induced by optical forces acting upon up to $10^5$ $^{87}$Rb atoms prepared in the lowest band of a one-dimensional intracavity optical lattice. The longevity of atomic motional coherence allows for strongly nonlinear optics at extremely low cavity photon numbers, as demonstrated by the observation of both branches of optical bistability at photon numbers below unity.
Free Electron Laser (FEL) and Collective Atomic Recoil Laser (CARL) are described by the same model of classical equations for properly defined scaled variables. These equations are extended to the quantum domain describing the particle's motion by a Schrödinger equation coupled to a self-consistent radiation field. The model depends on a single collective parameter $\bar ρ$ which represents the maximum number of photons emitted per particle. We demonstrate that the classical model is recovered in the limit $\bar ρ\gg 1$, in which the Wigner function associated to the Schrödinger equation obey…
Networks of globally coupled oscillators exhibit phase transitions from incoherent to coherent states. Atoms interacting with the counterpropagating modes of a unidirectionally pumped high-finesse ring cavity form such a globally coupled network. The coupling mechanism is provided by collective atomic recoil lasing (CARL), i.e. cooperative Bragg scattering of laser light at an atomic density grating, which is self-induced by the laser light. Under the rule of an additional friction force, the atomic ensemble is expected to undergo a phase transition to a state of synchronized atomic motion. We…
We determine the incoherent spectrum, squeezing properties and second-order correlation function of the collective atomic degrees of freedom in absorptive optical bistability. This is accomplished via a linearized Fokker-Planck equation in the positive P representation, guided by the analysis of [H. J. Carmichael, Phys. Rev. A 33, 3262 (1986)] which does not resort to adiabatic elimination. We focus on the regimes of weak and strong intracavity excitation, addressing the good-cavity and bad-cavity limits as well as the limit of collective strong coupling. Adiabatic elimination of the intracavi…
We propose an experiment to realize radiation to atom continuous variable quantum mapping, i.e. to teleport the quantum state of a single mode radiation field onto the collective state of atoms with a given momentum out of a Bose-Einstein condensate. The atoms-radiation entanglement needed for the teleportation protocol is established through the interaction of a single mode with the condensate in presence of a strong far off-resonant pump laser, whereas the coherent atomic displacement is obtained by the same interaction with the radiation in a classical coherent field. In principle, verifica…
We demonstrate clear collective atomic recoil motion in a dilute, momentum-squeezed, ultra-cold degenerate fermion gas by circumventing the effects of Pauli blocking. Although gain from bosonic stimulation is necessarily absent because the quantum gas obeys Fermi-Dirac statistics, collective atomic recoil motion from the underlying wave-mixing process is clearly visible. With a single pump pulse of the proper polarization, we observe two mutually-perpendicular wave-mixing processes occurring simultaneously. Our experiments also indicate that the red-blue pump detuning asymmetry observed with B…
We describe a method for non-degenerate four-wave mixing in a cold sample of 4-level atoms. An integral part of the four-wave mixing process is a collective instability which spontaneously generates a periodic density modulation in the cold atomic sample with a period equal to half of the wavelength of the generated high-frequency optical field. Due to the generation of this density modulation, phase-matching between the pump and scattered fields is not a necessary initial condition for this wave-mixing process to occur, rather the density modulation acts to "self phase-match" the fields durin…
We address the dynamics induced by collective atomic recoil in a Bose-Einstein condensate in presence of radiation losses and atomic decoherence. In particular, we focus on the linear regime of the lasing mechanism, and analyze the effects of losses and decoherence on the generation of entanglement. The dynamics is that of three bosons, two atomic modes interacting with a single-mode radiation field, coupled with a bath of oscillators. The resulting three-mode dissipative Master equation is solved analytically in terms of the Wigner function. We examine in details the two complementary limits …
We consider the effects of the trap environment on the atomic and optical quantum statistical properties and on the atom-photon correlations in the Collective Atomic-Recoil Laser. Atomic and optical statistical properties, as well as the atom-photon correlations are dependent on the optical field intensity and phase. In particular, depending on the values of the optical field intensity and phase, the fields statistics varies from coherent to superchaotic.
We present a wave atom optics theory of the Collective Atomic-Recoil Laser, where the atomic center-of-mass motion is treated quantum mechanically. It extends the previous ray atom optics theory, which treated the center-of-mass atomic motion classically, to the realm of ultracold atoms. For the case of a far off resonant pump laser we derive an analytical solution which gives the linear response of the CARL system for both the quantum and classical regimes. A linear stability analysis reveals significant qualitative differences between these two regimes, which arise from the effects of diffra…
An analytical perturbation theory of short-pulse, matter-wave superradiant scatterings is presented. We show that Bragg resonant enhancement is incapacitated and both positive and negative order scatterings contribute equally. We further show that propagation gain is small and scattering events primarily occur at the end of the condensate where the generated field has maximum strength, thereby explaining the apparent ``asymmetry" in the scattered components with respect to the condensate center. In addition, the generated field travels near the speed of light in a vacuum, resulting in signific…
We report on collective non-linear dynamics in an optical lattice formed inside a high finesse ring cavity in a so far unexplored regime, where the light shift per photon times the number of trapped atoms exceeds the cavity resonance linewidth. We observe bistability and self-induced squeezing oscillations resulting from the retro-action of the atoms upon the optical potential wells. We can well understand most of our observations within a simplified model assuming adiabaticity of the atomic motion. Non-adiabatic aspects of the atomic motion are reproduced by solving the complete system of cou…
We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in an…
We consider N driven two-level atoms interacting with a structured reservoir. By dressing the collective operators within a semiclassical approach, we derive a master equation and a mean-field single particle effective Hamiltonian. This Hamiltonian describes the optical bistability phenomenon occurring in the relation between an input electromagnetic field and the effective output generated by the N atoms. The dissipative part of the master equation and the effective single-particle Hamiltonian contain new terms due the reservoir structure of modes. In plotting the output field amplitude and p…
We calculate the steady-state and first-order time varying atom-field correlation functions in the weak-excitation limit of absorptive optical bistability from a linearized theory of quantum fluctuations. We formulate a Fokker-Planck equation in the positive P representation following the phase-space analysis of [H. J. Carmichael, Phys. Rev. A 33, 3262 (1986)] which is suitable for the determination of cross-correlations as it does not resort to adiabatic elimination. Special emphasis is placed on the limit of collective strong coupling as attained from a vanishing photon-loss rate. We compare…
The Dicke model is a paradigmatic quantum-optical model describing the interaction of a collection of two-level systems with a single bosonic mode. Effective implementations of this model made it possible to observe the emergence of superradiance, i.e., cooperative phenomena arising from the collective nature of light-matter interactions. Via reservoir engineering and analogue quantum simulation techniques, current experimental platforms allow us not only to implement the Dicke model, but also to design more exotic interactions, such as the two-photon Dicke model. In the Hamiltonian case, this…
A mean field theory for Raman superradiance (SR) with recoil is presented, where the typical SR signatures are recovered, such as quadratic dependence of the intensity on the number of atoms and inverse proportionality of the time scale to the number of atoms. A comparison with recent experiments and theories on Rayleigh SR and collective atomic recoil lasing (CARL) are included. The role of recoil is shown to be in the decay of atomic coherence and breaking of the symmetry of the SR end-fire modes.
We determine the transmission of light through a planar atomic array beyond the limit of low light intensity that displays optical bistability in the mean-field regime. We develop a theory describing the intrinsic optical bistability, which is supported purely by resonant dipole-dipole interactions in free space, showing how bistable light amplitudes exhibit both strong cooperative and weak single-atom responses and how they depend on the underlying low light intensity collective excitation eigenmodes. Similarities of the theory with optical bistability in cavities are highlighted, while recur…
Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driv…
We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and applies equally well to distinguishable and indistinguishable atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find closed-form formulas for a number of relevant states (Gaussia…
Ultracold atoms interacting with the optical modes of a high-Q optical ring cavity can synchronize their motion. The collective behavior makes the system interesting for quantum computing applications. This paper is devoted to the study of the collective coupling. We report on the first observation of a collective dynamics and on the realization of a laser, the gain mechanism of which is based on collective atomic recoil. We show that, if the atoms are subject to a friction force, starting from an unordered distribution they spontaneously form a moving density grating. Furthermore, we demonstr…
In many experiments isolated atoms and ions have been inserted into high-finesse optical resonators for the study of fundamental quantum optics and quantum information. Here, we introduce another application of such a system, as the realization of cavity optomechanics where the collective motion of an atomic ensemble serves the role of a moveable optical element in an optical resonator. Compared with other optomechanical systems, such as those incorporating nanofabricated cantilevers or the large cavity mirrors of gravitational observatories, our cold-atom realization offers direct access to t…
We report on the observation of collective atomic recoil lasing and superradiant Rayleigh scattering with ultracold and Bose-Einstein condensed atoms in an optical ring cavity. Both phenomena are based on instabilities evoked by the collective interaction of light with cold atomic gases. This publication clarifies the link between the two effects. The observation of superradiant behavior with thermal clouds as hot as several tens of $μ\textrm{K}$ proves that the phenomena are driven by the cooperative dynamics of the atoms, which is strongly enhanced by the presence of the ring cavity.
Collective interaction of light with an atomic gas can give rise to superradiant instabilities. We experimentally study the sudden build-up of a reverse light field in a laser-driven high-finesse ring cavity filled with ultracold thermal or condensed atoms. While superradiant Rayleigh scattering from atomic clouds is normally only observed at very low temperatures (i.e. well below $1 μ$K), the presence of the ring cavity enhances cooperativity and allows for superradiance with thermal clouds as hot as several $10 μ$K. A characterization of the superradiance at various temperatures and cooperat…
A superfluid atomic gas is prepared inside an optical resonator with an ultra-narrow band width 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 accelerat…
It is well known that in the presence of a ring cavity the light scattering from a uniform atomic ensemble can become unstable resulting in the collective atomic recoil lasing. This is the result of a positive feedback due to the cavity. We propose to add an additional electronic feedback loop based on the photodetection of the scattered light. The advantage is a great flexibility in choosing the feedback algorithm, since manipulations with electric signals are very well developed. In this paper we address the application of such a feedback to atoms in the Bose-Einstein condensed state and exp…
The collective dynamics of mobile scatterers and light in optical resonators generates complex behaviour. For strong transverse illumination a phase transition from homogeneous to crystalline particle order appears. In contrast, a gas inside a single-side pumped ring cavity exhibits an instability towards bunching and collective acceleration called collective atomic recoil lasing (CARL). We demonstrate that by driving two orthogonally polarized counter propagating modes of a ring resonator one realises both cases within one system. The corresponding phase diagram depending on the two pump inte…
Ultra cold fermionic atoms placed in a synthetic magnetic field arrange themselves in Landau levels. We theoretically study the optomechanical interaction between the light field and collective excitations of such fermionic atoms in synthetic magnetic field by placing them in side a Fabry Perot cavity. We derive the effective hamiltonian for particle hole excitations from a filled Landau level using a bosonization technique and obtain an expression for the cavity transmission spectrum. Using this we show that the cavity transmission spectrum demonstrates cold atom analogue of Subnikov de Hass …
Cooperative spontaneous emission of a single photon from a cloud of N atoms modifies substantially the radiation pressure exerted by a far-detuned laser beam exciting the atoms. On one hand, the force induced by photon absorption depends on the collective decay rate of the excited atomic state. On the other hand, directional spontaneous emission counteracts the recoil induced by the absorption. We derive an analytical expression for the radiation pressure in steady-state. For a smooth extended atomic distribution we show that the radiation pressure depends on the atom number via cooperative sc…
