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arXiv:cond-mat/9905425 · Physical Review Letters

Theory of Superradiant Scattering of Laser Light from Bose-Einstein Condensates

M. G. Moore, Pierre Meystre

Published Dec 20, 1999• 185 citations
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Abstract

In a recent MIT experiment, a new form of superradiant Rayleigh scattering was observed in Bose-Einstein condensates. We present a detailed theory of this phenomenon in which condensate depletion leads to mode competition, which, together with the directional dependence of the scattering rate, is ultimately responsible for the observed phenomena. The nonlinear response of the system is shown to be highly sensitive to initial quantum fluctuations which cause large run to run variations in the observed superradiant pulses.

DOI
10.1103/physrevlett.83.5202

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In a recent MIT experiment, a new form of superradiant Rayleigh scattering was observed in Bose-Einstein condensates. We present a detailed theory of this phenomenon in which condensate depletion leads to mode competition, which, together with the directional dependence of the scattering rate, is ultimately responsible for the observed phenomena. The nonlinear response of the system is shown to be highly sensitive to initial quantum fluctuations which cause large run to run variations in the observed superradiant pulses.
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The superradiant Rayleigh scattering of high-intensity light pulses by the Bose-Einstein condensate of rubidium vapor is studied using the model proposed earlier. It is demonstrated that four states with a certain momentum are occupied under the experimental conditions (two states correspond to the forward recoil and two others correspond to the backward recoil). Condensate pulsations between the zero-momentum state and the above states are detected and studied. The corresponding shape of the coherent Rayleigh pulse is found.
A theory of coherent light scattering from an elongated Bose-Einstein condensate exposed to an off-resonant laser beam is presented. The model describes the emission of two superradiant pulses along the sample's major axis simultaneous with the formation of a bidimensional atomic grating inside the sample, as was observed in a recent MIT experiment [Inouye, S. et al., 1999, Science, 285, 571]. We predictions of the semiclassical model, in which the atomic motion is treated classically, are compared with these of the quantum model, obtained including the quantum mechanical description of the atomic motion. In the quantum limit the superradiant regime becomes a sequential process, in which during each collective scattering atoms emit a it hyperbolic secant pulse and populate an adjacent momentum state.
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.
Due to its coherence properties and high optical depth, a Bose–Einstein condensate [BEC] provides an ideal setting to investigate collective atom-light interactions. Superradiant light scattering [SLS] in a BEC is a fascinating example of such an interaction. It is an analogous process to Dicke superradiance, in which an electronically inverted sample decays collectively, leading to the emission of one or more light pulses in a well-defined direction. Through time-resolved measurements of the superradiant light pulses emitted by an end-pumped BEC, we study the close connection of SLS with Dicke superradiance. A 1D model of the system yields good agreement with the experimental data and shows that the dynamics result from the structures that build up in the light and matter-wave fields along the BEC. This paves the way for exploiting the atom–photon correlations generated by the superradiance.