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arXiv:quant-ph/0208100 · Physical Review Letters

Observation of Collective-Emission-Induced Cooling of Atoms in an Optical Cavity

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

Published Feb 14, 2003• 150 citations
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Abstract

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 $1500\text{ }\text{ }\mathrm{m}/{\mathrm{s}}^{2}$ 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.

DOI
10.1103/physrevlett.90.063003

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We report the observation of collective-emission-induced, velocity-dependent light forces. One-third of a falling sample containing 3\ifmmode×\else\texttimes\fi1063\ifmmode\times\else\texttimes\fi{}{10}^{6}3\ifmmode×\else\texttimes\fi106 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 \ensuremathμK7\text{ }\ensuremath{\mu}\mathrm{K}7 \ensuremathμK, well below the free-space Doppler limit. The measured forces substantially exceed those predicted for a single two-level atom.
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 review the modifications and implications of the effect of light forces on atoms when the field is enclosed in an optical resonator of high finesse. The systems considered range from a single atom strongly coupled to a single mode of a high-Q microcavity to a large ensemble of atoms in a highly degenerate quasi-confocal resonator. We set up general models that allow us to obtain analytic expressions for the optical potential, friction, and diffusion. In the bad-cavity limit the modified cooling properties can be attributed to the spectral modifications of light absorption and spontaneous emission in a form of generalized and enhanced Doppler cooling. For the strong coupling regime in a good cavity, we identify the dynamical coupling between the light field intensity and the atomic motion as the central mechanism underlying the cavity-induced cooling. The dynamical cavity cooling, which does not rely on spontaneous emission, can be enhanced by multimode cavity geometries because of the effect of coherent photon redistribution between different modes. The model is then generalized to include several distinct frequencies to account for more general trap geometries. Finally we show that the field-induced buildup of correlations between the motion of different particles plays a central role in the scaling behavior of the system. Depending on the geometry and parameters, its effect ranges from strong destructive interference, slowing down the cooling process, to self-organized crystallization, implying atomic self-trapping and faster cooling to lower temperatures by cooperative coherent scattering.
We theoretically investigate the correlated dynamics of N coherently driven atoms coupled to a standing-wave cavity mode. For red detuning between the driving field and the cavity as well as the atomic resonance frequencies, we predict a light force induced self-organization of the atoms into one of two possible regular patterns, which maximize the cooperative scattering of light into the cavity field. Kinetic energy is extracted from the atoms by superradiant light scattering to reach a final kinetic energy related to the cavity linewidth. The self-organization starts only above a threshold of the pump strength and atom number. We find a quadratic dependence of the cavity mode intensity on the atom number, which demonstrates the cooperative effect.
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 present a microscopic laser model for many atoms coupled to a single-cavity mode, including the light forces, which result from atom-field momentum exchange. Within a semiclassical description, we solve the equations for the atomic motion and the internal dynamics to obtain analytic expressions for the optical potential and the friction force seen by each atom. When optical gain is maximum at frequencies where the light field extracts kinetic energy from the atomic motion, the dynamics combines optical lasing and motional cooling. From the corresponding momentum-diffusion coefficient we predict sub-Doppler temperatures in the stationary state. This generalizes the theory of cavity-enhanced laser cooling to active cavity systems. We identify the gain-induced reduction of the effective resonator linewidth as the key origin for the faster cooling and the lower temperatures, which implies that a bad cavity with a gain medium can replace a high-QQQ cavity. In addition, this shows the importance of light forces for gas lasers in the low-temperature limit, where atoms can arrange in a periodic pattern maximizing gain and counteracting spatial hole burning. Ultimately, in the low-temperature limit, such a setup should allow us to combine optical lasing and atom lasing in a single device.
The optical forces exerted on a slowly moving two-level atom in a standing wave are profoundly modified when the normal decay rates of the atom are altered. The theory presented in this paper shows that the stimulated emission force becomes dominant at a very low laser intensity. Furthermore, it can change sign to provide an additional cooling force instead of a heating force at laser detunings below the atomic resonance. These phenomena can lead to equilibrium temperatures below the Doppler limit.