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Physical Review Letters

Observation of Collective Friction Forces due to Spatial Self-Organization of Atoms: From Rayleigh to Bragg Scattering

Adam T. Black, Hilton W. Chan, Vladan Vuletić

Published Nov 11, 2003• 353 citations
Publisher

Abstract

We demonstrate that emission-induced self-organization of two-level atoms can effect strong damping of the sample's center-of-mass motion. When illuminated by far-detuned light, cold cesium atoms assemble into a density grating that efficiently diffracts the incident light into an optical resonator. We observe random phase jumps of pi in the emitted light, confirming spontaneous symmetry breaking in the atomic self-organization. The Bragg diffraction results in a collective friction force with center-of-mass deceleration up to 1000 m/s(2) that is effective even for an open atomic transition.

DOI
10.1103/physrevlett.91.203001

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We demonstrate that emission-induced self-organization of two-level atoms can effect strong damping of the sample's center-of-mass motion. When illuminated by far-detuned light, cold cesium atoms assemble into a density grating that efficiently diffracts the incident light into an optical resonator. We observe random phase jumps of pi in the emitted light, confirming spontaneous symmetry breaking in the atomic self-organization. The Bragg diffraction results in a collective friction force with center-of-mass deceleration up to 1000 m/s(2) that is effective even for an open atomic transition.
We report on a novel type of collective friction force acting on the center-of-mass motion of a self-organizing atomic sample inside a resonator. The force substantially exceeds the sum of the light forces acting on isolated atoms. We also observe spontaneous symmetry breaking between two equivalent, but spatially oset self-organization patterns in the standing wave resonator, as predicted by Domokos and Ritsch. We identify and experimentally verify the dependencies of the threshold for the self-organization process on incident-light and atomic sample properties. 1 Introduction: Single-atom versus collective light forces The well-known light-induced forces on atoms, such as the conservative dipole force, or the dissipative Doppler and polarization gradient forces 1, arise from the inter-action of the incident light with single atoms. Collective parameters characterizing the sample, such as the number of atoms, their spatial or momentum distribution
We report the observation of collective-emission-induced, velocity-dependent light forces. One-third of a falling sample containing $3\ifmmode\times\else\texttimes\fi{}{10}^{6}$ cesium atoms illuminated by a horizontal standing wave is stopped by cooperatively emitting light into a vertically oriented, confocal resonator. We observe decelerations up to 1500  m/s21500\text{ }\text{ }\mathrm{m}/{\mathrm{s}}^{2}1500  m/s2 and cooling to temperatures as low as $7\text{ }\ensuremath{\mu}\mathrm{K}$, well below the free-space Doppler limit. The measured forces substantially exceed those predicted for a single two-level atom.
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.
Pattern formation of atoms in high-finesse optical resonators results from the mechanical forces of light associated with superradiant scattering into the cavity mode. It occurs when the laser intensity exceeds a threshold value such that the pumping processes counteract the losses. We consider atoms driven by a laser and coupling with a mode of a standing-wave cavity and describe their dynamics with a Fokker-Planck equation, in which the atomic motion is semiclassical but the cavity field is a full quantum variable. The asymptotic state of the atoms is a thermal state, whose temperature is solely controlled by the detuning between the laser and the cavity frequency and by the cavity loss rate. From this result we derive the free energy and show that in the thermodynamic limit self-organization is a second-order phase transition. The order parameter is the field inside the resonator to which one can associate a magnetization in analogy to ferromagnetism, the control field is the laser intensity, but the steady state is intrinsically out of equilibrium. In the symmetry-broken phase, quantum noise induces jumps of the spatial density between two ordered patterns: We characterize the statistical properties of this temporal behavior at steady state and show that the thermodynamic properties of the system can be extracted by detecting the light at the cavity output. The results of our analysis are in full agreement with previous studies; we extend them by deriving a self-consistent theory which is valid also when the cavity field is in the shot-noise limit and elucidate the nature of the self-organization transition.
We study resonator-induced light forces arising from cooperative atom–light interaction. For such collective processes, the force on the sample can be orders of magnitude larger than the sum of conventional light forces on individual atoms. Since resonator-induced light forces can be dissipative even when the incident light is far detuned from atomic transitions, they may be applicable to target particles with a complex level structure. (Some figures in this article are in colour only in the electronic version)
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.