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arXiv:quant-ph/0402013 · Physical Review Letters

Self-Synchronization and Dissipation-Induced Threshold in Collective Atomic Recoil Lasing

C. von Cube, Sebastian Slama, Dietmar Kruse, Claus Zimmermann, Ph. W. Courteille, Gordon R. M. Robb, N. Piovella, R. Bonifacio

Published Aug 16, 2004• 83 citations
arXivHTMLPDF

Abstract

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, 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 present the experimental investigation of this phase transition by studying the threshold behavior of this lasing process.

DOI
10.1103/physrevlett.93.083601

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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, 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 present the experimental investigation of this phase transition by studying the threshold behavior of this lasing process.
An ensemble of periodically ordered atoms coherently scatters the light of an incident laser beam. The scattered and the incident light may interfere and give rise to a light intensity modulation and thus to optical dipole forces which, in turn, emphasize the atomic ordering. This positive feedback is at the origin of the collective atomic recoil laser (CARL). We demonstrate this dynamics using ultracold atoms confined by dipole forces in a unidirectionally pumped far red‐detuned high‐finesse optical ring cavity. Under the influence of an additional dissipative force exerted by an optical molasses the atoms, starting from an unordered distribution, spontaneously form a density grating moving at constant velocity. Additionally, steady state lasing is observed in the reverse direction if the pump laser power exceeds a certain threshold. We compare the dynamics of the atomic trajectories to the behavior of globally coupled oscillators, which exhibit phase transitions from incoherent to coherent states if the coupling strength exceeds a critical value.
Abstract 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 demonstrate that a 1D atomic density grating can be probed via Bragg scattering. By heterodyning the Bragg‐reflected light with a reference beam, we obtain detailed information on phase shifts induced by the Bragg scattering process.
A cloud of ultra-cold atoms is loaded into the attractive potential of a light wave that is generated by two counter-propagating modes of a high-finesse ring resonator. The two modes are coupled by the atoms due to coherent Rayleigh scattering and generate a potential which acts back on the motion of the atoms. This feedback leads to a new frequency component and can be described in terms of the long time proposed collective atomic recoil laser (CARL). This model is investigated experimentally and extended by introducing an optical friction force acting on the atoms. This allows for steady state operation of the CARL. Furthermore, it leads to a threshold behaviour of the CARL that translates into a novel type of phase transition: while passing the threshold the initially homogeneous atomic distribution is bunched in space and velocity. With this behaviour the system turns out to acquire some of the main features of the so-called Kuramoto model which provides a very general description of a network of limit cycle oscillators.
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.
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.
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.