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arXiv:1411.4519 · Europhysics Letters (EPL)

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

Stefan Ostermann, T. Grießer, Helmut Ritsch

Published Feb 1, 2015• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1209/0295-5075/109/43001

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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.
Cold atoms in optical high‐Q cavities are an ideal model system for long‐range interacting particles. The position of two arbitrary atoms is, independent on their distance, coupled by the back‐scattering of photons within the cavity. This mutual coupling can lead to collective instability and self‐organization of a cloud of cold atoms interacting with the cavity fields. This phenomenon (CARL, i.e. Collective Atomic Recoil Lasing) has been discussed theoretically for years, but was observed only recently in our lab. The CARL‐effect is closely linked to superradiant Rayleigh scattering, which has been intensely studied with Bose‐Einstein condensates in free space. By adding a resonator the coherence time of the system, in which the instability occurs, can be strongly enhanced. This enables us to observe cavity‐enhanced superradiance with both Bose‐Einstein condensates and thermal clouds and allows us to close the discussion about the role of quantum statistics in superradiant scattering.
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.
A gas of linearly polarizable particles transversely pumped by an off-resonant laser and interacting with the counterpropagating radiation modes of a ring cavity is studied. Depending on the pump intensity and the detunings the gas can form a self-organized density grating that enhances the feeding of the cavity. We investigate the system via a mean-field approach and find the thermodynamic phases of i) uniform distribution, ii) self-organized Bragg lattice, iii) lattice with defects, and iv) instability. The occurrence of these phases as a function of the pump intensity and particle density is fully mapped.
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.
We study the dynamics of a fast gaseous beam in a high Q ring cavity counter propagating a strong pump laser with large detuning from any particle optical resonance. As spontaneous emission is strongly suppressed the particles can be treated as polarizable point masses forming a dynamic moving mirror. Above a threshold intensity the particles exhibit spatial periodic ordering enhancing collective coherent backscattering which decelerates the beam. Based on a linear stability analysis in their accelerated rest frame we derive analytic bounds for the intensity threshold of this selforganization as a function of particle number, average velocity, kinetic temperature, pump detuning and resonator linewidth. The analytical results agree well with time dependent simulations of the N-particle motion including field damping and spontaneous emission noise. Our results give conditions which may be easily evaluated for stopping and cooling a fast molecular beam.