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Laser Spectroscopy

SELF-ORGANIZATION OF ATOMIC SAMPLES IN RESONATORS AND COLLECTIVE LIGHT FORCES

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

Published Feb 1, 2004• 1 citation
Publisher

Abstract

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

DOI
10.1142/9789812703002_0051

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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 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.
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 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 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)
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.
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.