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arXiv:cond-mat/0511018 · Physical Review A

Dynamics of matter-wave and optical fields in superradiant scattering from Bose-Einstein condensates

O. Zobay, Georgios M. Nikolopoulos

Published Oct 27, 2005• 39 citations
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Abstract

We study superradiant scattering off Bose-Einstein condensates by solving the semiclassical Maxwell-Schr\"odinger equations describing the coupled dynamics of matter-wave and optical fields. Taking the spatial dependence of these fields along the condensate axis into account, we are able to reproduce and explain many of the characteristic features observed in the experiments of Inouye et al. [Science 285, 571 (1999)] and Schneble et al. [Science 300, 475 (2003)], such as the shape of the atomic side-mode distributions for forward and backward scattering, the spatial asymmetry between forward and backward side modes, and the depletion of the condensate center observed for forward scattering.

DOI
10.1103/physreva.72.041604

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We study superradiant scattering off Bose-Einstein condensates by solving the semiclassical Maxwell-Schr"odinger equations describing the coupled dynamics of matter-wave and optical fields. Taking the spatial dependence of these fields along the condensate axis into account, we are able to reproduce and explain many of the characteristic features observed in the experiments of Inouye et al. [Science 285, 571 (1999)] and Schneble et al. [Science 300, 475 (2003)], such as the shape of the atomic side-mode distributions for forward and backward scattering, the spatial asymmetry between forward and backward side modes, and the depletion of the condensate center observed for forward scattering.
We present a detailed theoretical analysis of superradiant Rayleigh scattering from atomic Bose-Einstein condensates. A thorough investigation of the spatially resolved time evolution of optical and matter-wave fields is performed in the framework of the semiclassical Maxwell-Schr\"odinger equations. Our theory is not only able to explain many of the known experimental observations, e.g., the behavior of the atomic side-mode distributions, but also provides further detailed insights into the coupled dynamics of optical and matter-wave fields. To work out the significance of propagation effects, we compare our results to other theoretical models in which these effects are neglected.
We theoretically discuss several aspects of sequential superradiant scattering from atomic Bose-Einstein condensates. Our treatment is based on the semiclassical description of the process in terms of the Maxwell-Schrödinger equations for coupled matter-wave and optical fields. First, we investigate sequential scattering in the weak-pulse regime and work out the essential mechanisms responsible for bringing about the characteristic fan-shaped side-mode distribution patterns. Second, we discuss the transition between the Kapitza-Dirac and Bragg regimes of sequential scattering in the strong-pulse regime. Finally, we consider the situation where superradiance is initiated by coherently populating an atomic side mode through Bragg diffraction, as in studies of matter-wave amplification, and describe the effect on the sequential scattering process.
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.