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arXiv:0805.0039 · Physical Review A

Superradiant Raman scattering in an ultracold Bose gas at finite temperature

Hermann Uys, Pierre Meystre

Published Jun 16, 2008• 10 citations
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Abstract

We study superradiant Raman scattering from an ultracold, but finite, temperature Bose gas in a harmonic trap. Numerical simulations indicate the existence of distinct time scales associated with the decoherence of the condensed versus thermal fractions, and the concomitant preferred scattering from atoms in low-lying trap states in the regime where superradiance takes place on a time scale comparable to an inverse trap frequency. As a consequence the scattered atoms experience a modest reduction in temperature as compared to the unscattered atoms.

DOI
10.1103/physreva.77.063614

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We study superradiant Raman scattering from an ultracold, but finite, temperature Bose gas in a harmonic trap. Numerical simulations indicate the existence of distinct time scales associated with the decoherence of the condensed versus thermal fractions, and the concomitant preferred scattering from atoms in low-lying trap states in the regime where superradiance takes place on a time scale comparable to an inverse trap frequency. As a consequence the scattered atoms experience a modest reduction in temperature as compared to the unscattered atoms.
We present an overview of our recent work describing the treatment of ultracold atomic Bose gases confined to two dimensions in a harmonic trap. We show how the gas goes through a number of regimes as the axially confining potential is increased and discuss the scattering properties of the gas in each of these regimes. We then use the formalism developed to investigate the phase-coherent Bose-Einstein condensate that is present in the trapped two-dimensional gas at temperatures that are low compared to the ideal gas critical temperature and to analyze the first-order coherence as a function of temperature. We identify the regime in which the gas loses its global phase coherence, although a macroscopic occupation of the ground state persists at a temperature well below the ideal gas critical temperature. We comment on the possible connection between this fluctuating regime and the Berezinskii-Kosterlitz-Thouless phase.
We propose different spectroscopic methods to explore the nature of the thermal excitations of a trapped Bose condensed gas: 1) a four photon process to probe the uniform region in the trap center: 2) a stimulated Raman process in order to analyze the influence of a momentum transfer in the resulting scattered atom momentum distribution. We apply these methods to address specifically the energy spectrum and the scattering amplitude of these excitations in a transition between two hyperfine levels of the gas atoms. In particular, we exemplify the potential offered by these proposed techniques by contrasting the spectrum expected from the non-conserving Bogoliubov approximation, valid for weak depletion, to the spectrum of the finite-temperature extensions like the conserving generalized random phase approximation (GRPA). Both predict the existence of the Bogoliubov collective excitations but the GRPA approximation distinguishes them from the single-atom excitations with a gapped and parabolic dispersion relation and accounts for the dynamical screening of any external perturbation applied to the gas. We present two feasible experiments, one concerns the observation of the gap associated to this second branch of excitations and the other deals with this screening effect.
We propose an alternative formulation for atomic side mode dynamics from superradiant light scattering of trapped atoms. A detailed analysis of the recently observed superradiant light scattering from trapped Bose gases [S. Inouye et al., Science 285, 571 (1999)] is presented. We find that scattered light intensity can exhibit both oscillatory and exponential growth behaviors depending on densities, pump pulse characteristics, temperatures, and geometric shapes of trapped gas samples. The total photon scattering rate as well as the accompanying matter wave amplification depend explicitly on atom number fluctuations in the condensate. Our formulation allows for natural and transparent interpretations of subtle features in the experimental data, and provides numerical simulations in good agreement with most important aspects of the experimental observations.
We study the condensed fraction of a harmonically trapped atomic Bose gas at the critical point predicted by mean-field theory. The nonzero condensed fraction f(0) is induced by critical correlations which increase the transition temperature T(c) above T(c) (MF). Unlike the T(c) shift in a trapped gas, f(0) is sensitive only to the critical behavior in the quasiuniform part of the cloud near the trap center. To leading order in the interaction parameter a/λ(0), where a is the s-wave scattering length and λ(0) the thermal wavelength, we expect a universal scaling f(0) proportionally (a/λ(0))(4). We experimentally verify this scaling using a Feshbach resonance to tune a/λ(0). Further, using the local density approximation, we compare our measurements with the universal result obtained from Monte Carlo simulations for a uniform system, and find excellent quantitative agreement.
Superradiance and coherent atomic recoil lasing are two closely related phenomena, both resulting from the cooperative scattering of light by atoms. In ultracold atomic gases below the critical temperature for Bose-Einstein condensation these processes take place with the simultaneous amplification of the atomic matter waves. We explore these phenomena by surveying some of the experimental and theoretical developments that have emerged in this field of study since the first observation of superradiant scattering from a Bose-Einstein condensate in 1999 [1].