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Europhysics Letters (EPL)

Self-organization of a laser-driven cold gas in a ring cavity

D Nagy, János K. Asbóth, P. Domokos, Helmut Ritsch

Published Mar 7, 2006• 43 citations
Publisher

Abstract

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.

DOI
10.1209/epl/i2005-10521-4

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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.
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.
We study a transversely pumped atomic Bose-Einstein condensate coupled to a single-mode optical cavity, where effective atom-atom interactions are mediated by pump and cavity photons. A number of experiments and theoretical works have shown the formation of a superradiant state in this setup, where interference of pump and cavity light leads to an optical lattice in which atoms self-consistently organize. This self-organization has been extensively studied using the approximate Dicke model (truncating to two momentum states), as well as through numerical Gross-Pitaevskii simulations in one and two dimensions. Here, we perform a full mean-field analysis of the system, including all relevant atomic momentum states and the cavity field. We map out the steady-state phase diagram vs pump strength and cavity detuning, and provide an in-depth understanding of the instabilities that are linked to the emergence of spatiotemporal patterns. We find and describe parameter regimes where the mean field predicts bistability, regimes where the dynamics form chaotic trajectories, instabilities caused by resonances between normal mode excitations, and states with atomic dynamics but vanishing cavity field.
A cold dilute atomic gas in an optical resonator can be radiatively cooled by coherent scattering processes when the driving laser frequency is tuned close to but below the cavity resonance. When the atoms are sufficiently illuminated, their steady state undergoes a phase transition from a homogeneous distribution to a spatially organized Bragg grating. We characterize the dynamics of this self-ordering process in the semi-classical regime when distinct cavity modes with commensurate wavelengths are quasi-resonantly driven by laser fields via scattering by the atoms. The lasers are simultaneously applied and uniformly illuminate the atoms; their frequencies are chosen so that the atoms are cooled by the radiative processes, and their intensities are either suddenly switched or slowly ramped across the self-ordering transition. Numerical simulations for different ramp protocols predict that the system will exhibit long-lived metastable states, whose occurrence strongly depends on the initial temperature, ramp speed, and the number of atoms.
Cold atoms, driven by a laser and simultaneously coupled to the quantum field of an optical resonator, may self-organize in periodic structures. These structures are supported by the optical lattice, which emerges from the laser light they scatter into the cavity mode and form when the laser intensity exceeds a threshold value. We study theoretically the quantum ground state of these structures above the pump threshold of self-organization by mapping the atomic dynamics of the self-organized crystal to a Bose-Hubbard model. We find that the quantum ground state of the self-organized structure can be the one of a Mott insulator, depending on the pump strength of the driving laser. For very large pump strengths, where the intracavity-field intensity is maximum and one would expect a Mott-insulator state, we find intervals of parameters where the phase is compressible. These states could be realized in existing experimental setups.
Optomechanical pattern forming instabilities in a cloud of cold atoms lead to self-organized spatial structures of light and atoms. Here, we consider the optomechanical self-structuring of a cold atomic cloud in the presence of a phase structured input field, carrying orbital angular momentum. For a planar ring cavity setup, a model of coupled cavity field and atomic density equations describes a wide range of drifting modulation instabilities in the transverse plane. This leads to the formation of rotating self-organized rings of light-atom lattices. Using linear stability analysis and numerical simulations of the coupled atomic and optical dynamics, we demonstrate the presence of macroscopic atomic transport corresponding to the pattern rotation, induced by the structured pump phase profile.
We present a detailed study of the spatial self-organization of laser-driven atoms in an optical cavity, an effect predicted on the basis of numerical simulations [P. Domokos and H. Ritsch, Phys. Rev. Lett. 89, 253003 (2002)] and observed experimentally [A. T. Black et al., Phys. Rev. Lett. 91, 203001 (2003)]. Above a threshold in the driving laser intensity, from a uniform distribution the atoms evolve into one of two stable patterns that produce superradiant scattering into the cavity. We derive analytic formulas for the threshold and critical exponent of this phase transition from a mean-field approach. Numerical simulations of the microscopic dynamics reveal that, on a laboratory time scale, a hysteresis masks the mean-field behavior. Simple physical arguments explain this phenomenon and provide analytical expressions for the observable threshold. Above a certain density of the atoms a limited number of ``defects'' appear in the organized phase and influence the statistical properties of the system. The scaling of the cavity cooling mechanism and the phase-space density with the atom number is also studied.