Collective Atomic Recoil Laser Research Articles

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.

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.

Two-Photon Collective Atomic Recoil Lasing

We present a theoretical study of the interaction between light and a cold gasof three-level, ladder configuration atoms close to two-photon resonance. In particular, weinvestigate the existence of collective atomic recoil lasing (CARL) instabilities in differentregimes of internal atomic excitation and compare to previous studies of the CARL instabilityinvolving two-level atoms. In the case of two-level atoms, the CARL instability is quenchedat high pump rates with significant atomic excitation by saturation of the (one-photon)coherence, which produces the optical forces responsible for the instability and rapid heatingdue to high spontaneous emission rates. We show that in the two-photon CARL schemestudied here involving three-level atoms, CARL instabilities can survive at high pump rateswhen the atoms have significant excitation, due to the contributions to the optical forces frommultiple coherences and the reduction of spontaneous emission due to transitions betweenthe populated states being dipole forbidden. This two-photon CARL scheme may form thebasis of methods to increase the effective nonlinear optical response of cold atomic gases.

Stability diagram of the collective atomic recoil laser with thermal atoms

We experimentally investigate cold thermal atoms in a single sidedly pumped optical ring resonator for temperatures between 0.4 and $9\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$. The threshold for collective atomic recoil lasing (CARL) is recorded for various pump-cavity detunings. The resulting stability diagram is interpreted by simulating the classical CARL equations. We find that the stability diagram for thermal atoms shows the same asymmetry as observed for Bose-Einstein condensates in previous experiments. Whereas for condensates the asymmetry is well explained by a Dicke-type quantum model we here discuss a simplified classical model. It complements the quantum model and provides an intuitive explanation based on the change in the long-range atomic interaction with pump-cavity detuning.

Atomic self-ordering in a ring cavity with counterpropagating pump fields

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, cold particles inside a single-side pumped ring cavity exhibit an instability towards bunching and collective acceleration called collective atomic recoil lasing (CARL). We demonstrate that by driving two orthogonally polarized counterpropagating modes of a ring resonator one realises both cases within one system. As a function of the two pump intensities the corresponding phase diagram exhibits regions in which either a generalized form of self-ordering towards a travelling density wave with constant centre-of-mass velocity or a CARL instability is formed. Time-dependent control of the cavity driving then allows to accelerate or slow down and trap a sufficiently dense beam of linearly polarizable particles.

Mode-locked Bloch oscillations in a ring cavity

We present a new technique for stabilizing and monitoring Bloch oscillations of ultracold atoms in an optical lattice under the action of a constant external force. In the proposed scheme, the atoms also interact with a unidirectionally pumped optical ring cavity whose one arm is collinear with the optical lattice. For weak collective coupling, Bloch oscillations dominate over the collective atomic recoil lasing instability and develop a synchronized regime in which the atoms periodically exchange momentum with the cavity field.

Controlled generation of momentum states in a high-finesse ring cavity

A Bose-Einstein condensate in a high-finesse ring cavity scatters the photons of a pump beam into counterpropagating cavity modes, populating a bi-dimensional momentum lattice. A high-finesse ring cavity with a sub-recoil linewidth allows to control the quantized atomic motion, selecting particular discrete momentum states and generating atom-photon entanglement. The semiclassical and quantum model for the 2D collective atomic recoil lasing (CARL) are derived and the superradiant and good-cavity regimes discussed. For pump incidence perpendicular to the cavity axis, the momentum lattice is symmetrically populated. Conversely, for oblique pump incidence the motion along the two recoil directions is unbalanced and different momentum states can be populated on demand by tuning the pump frequency.

Experimental perspectives for systems based on long-range interactions

The possibility of observing phenomena peculiar to long-range interactions, and morespecifically in the so-called quasi-stationary state (QSS) regime, is investigated within theframework of two devices, namely the free-electron laser (FEL) and the collectiveatomic recoil laser (CARL). The QSS dynamics has been mostly studied using theHamiltonian mean-field (HMF) toy model, demonstrating in particular the presence offirst-order and second-order out-of-equilibrium phase transitions from magnetized tounmagnetized regimes. Here, we give evidence of the strong connections between the HMFmodel and the dynamics of the two aforementioned devices, and we discuss theperspectives for observing some specific QSS features experimentally. In particular, adynamical analog of the phase transition is present in the FEL and in the CARL in itsconservative regime. As regards the dissipative CARL, a formal link is establishedwith the HMF model. For both FEL and CARL, calculations are performed withreference to existing experimental devices, namely the FERMI@Elettra FEL underconstruction at Sincrotrone Trieste (Italy) and the CARL system at LENS in Florence(Italy).

Cooperative atomic scattering of light from a laser with a colored noise spectrum

The collective atomic recoil lasing is studied for an ultra-cold and collisionless atomic gas in a partially coherent pump with a colored noise. Compared to white noise, correlations in colored noise are found to be able to greatly enhance or suppress the growth rate, above or below a critical detuning. Effects on cooperative scattering of light for noise correlation time, noise intensity and pump-probe detuning are discussed. This result is consistent with our simulation and linear analysis about the evolution equations in the regions of instability.

Enhancement of collective atomic recoil lasing due to pump phase modulation

We investigate the effect of a phase-modulated pump beam on collective backscattering [also termed collective atomic recoil lasing (CARL)] by a cold, collisionless atomic gas. We show using a numerical analysis that different regimes can be identified in which the atomic dynamics evolves in a qualitatively different manner during the light-atom interaction, depending on the magnitude of the pump modulation frequency. Our results also demonstrate that phase-modulating the pump field can substantially enhance the backscattered field intensity relative to the case of a monochromatic pump which has been used in CARL experiments to date.

Collective atomic recoil laser as a synchronization transition

We consider here a model previously introduced to describe the collective behavior of an ensemble of cold atoms interacting with a coherent electromagnetic field. The atomic motion along the self-generated spatially periodic force field can be interpreted as the rotation of a phase oscillator. This suggests a relationship with synchronization transitions occurring in globally coupled rotators. In fact, we show that whenever the field dynamics can be adiabatically eliminated, the model reduces to a self-consistent equation for the probability distribution of the atomic "phases." In this limit, there exists a formal equivalence with the Kuramoto model, though with important differences in the self-consistency conditions. Depending on the field-cavity detuning, we show that the onset of synchronized behavior may occur through either a first- or second-order phase transition. Furthermore, we find a secondary threshold, above which a periodic self-pulsing regime sets in, that is immediately followed by the unlocking of the forward-field frequency. At yet higher, but still experimentally meaningful, input intensities, irregular, chaotic oscillations may eventually appear. Finally, we derive a simpler model, involving only five scalar variables, which is able to reproduce the entire phenomenology exhibited by the original model.

Collective Atomic Recoil Lasing with a Partially Coherent Pump

We investigate the effect of pump phase noise on the collective backscattering of light by a cold, collisionless atomic gas. We show that for a partially coherent pump field, the growth rate of the backscattered field is reduced relative to that for a coherent pump, but the backscattered intensity can be increased. Our results demonstrate that fluctuations and noise can play a counterintuitive role in nonlocally coupled many-body systems.

Cavity-enhanced superradiant Rayleigh scattering with ultracold and Bose-Einstein condensed atoms

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 {mu}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.

A Wigner function model for free electron lasers

We derive a 1D quantum model for the free electron laser in terms of a Wigner function for the electron beam. We consider both the case of an unbounded space coordinate, for which the momentum is continuous, and the case of a periodic space coordinate, for which the momentum is discrete. The Wigner model extends the Schrödinger model, previously considered, since it also describes the evolution of a mixed state. Furthermore, the Wigner model shows explicitly the classical limit when the quantum FEL parameter ρ ¯ is large. This model is also the starting point for a future extension to a 3D description of the electron dynamics. The results obtained here are also valid for the quantum description of the collective atomic recoil laser.

Transverse effects in collective atomic recoil lasing

We investigate transverse effects in collective atomic recoil lasing (CARL), where a cold atomic sample is lightened by a far detuned laser beam resonant with the internal atomic transition. The gradient force of the scattered radiation field produces a collective self-focusing on the atoms, which could be observed in a Bose-Einstein condensate stored in a bidirectional optical ring cavity or in the superradiant CARL-BEC regime.

Superradiant Rayleigh Scattering and Collective Atomic Recoil Lasing in a Ring Cavity

Collective interaction of light with an atomic gas can give rise to superradiant instabilities. We experimentally study the sudden buildup of a reverse light field in a laser-driven high-finesse ring cavity filled with ultracold thermal or Bose-Einstein condensed atoms. While superradiant Rayleigh scattering from atomic clouds is normally observed only at very low temperatures (i.e., well below 1 microK), the presence of the ring cavity enhances cooperativity and allows for superradiance with thermal clouds as hot as several 10 microK. A characterization of the superradiance at various temperatures and cooperativity parameters allows us to link it to the collective atomic recoil laser.

Self-organization effects and light amplification of collective atomic recoil motion in a harmonic trap

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.

Theory for Raman superradiance in atomic gases

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.

Propagation effects in the quantum description of collective recoil lasing

The free electron laser and collective atomic recoil laser (CARL) are examples of collective recoil lasing, where exponential amplification of a radiation field occurs simultaneously with self-bunching of an ensemble of particles (electrons in the case of the FEL and atoms in the case of the CARL). In this paper, we discuss quantum and propagation effects using a model where the particle dynamics are described quantum-mechanically in terms of a matter-wave field, which evolves self-consistently with the radiation field. The model shows that the scattered radiation evolves superradiantly both in the case where the particle ensemble is short compared to the cooperation length of the system, and where the ensemble is long compared to the cooperation length. In both short and long pulse cases there exist a classical and quantum regime of superradiant emission. For short samples in both quantum and classical regimes the superradiant pulse has a low peak intensity and is said to exhibit ‘weak’ superradiance. For long pulses in both quantum and classical regimes of evolution, the dynamics at the rear edge of the sample is dominated by propagation. This produces a ‘strong’ superradiant pulse with much higher peak intensity than that predicted by ‘mean-field’ or ‘steady-state’ models in which propagation effects are neglected.