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Science

The Onset of Matter-Wave Amplification in a Superradiant Bose-Einstein Condensate

Dominik Schneble, Yoshio Torii, Micah Boyd, Erik W. Streed, David E. Pritchard, Wolfgang Ketterle

Published Apr 17, 2003• 187 citations
Publisher

Abstract

The interaction of short and strong laser pulses with an atomic Bose-Einstein condensate is found to generate patterns of recoiling atoms that are different from those seen in previous light-scattering experiments. This phenomenon can only be explained by optical stimulation, showing that the previous description of superradiance as atomic stimulation is incomplete and that matter-wave amplification in Bose-Einstein condensates is suppressed at short times. Our experiments clarify the nature of bosonic stimulation in the four-wave mixing of light and atoms.

DOI
10.1126/science.1083171

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The interaction of short and strong laser pulses with an atomic Bose-Einstein condensate is found to generate patterns of recoiling atoms that are different from those seen in previous light-scattering experiments. This phenomenon can only be explained by optical stimulation, showing that the previous description of superradiance as atomic stimulation is incomplete and that matter-wave amplification in Bose-Einstein condensates is suppressed at short times. Our experiments clarify the nature of bosonic stimulation in the four-wave mixing of light and atoms.
In this paper, we consider two models which exhibit equilibrium BEC superradiance. They are related to two different types of superradiant scattering observed in recent experiments. The first one corresponds to the amplification of matter waves due to Raman superradiant scattering from a BE condensate, when the recoiled and the condensed atoms are in different internal states. The main mechanism is stimulated Raman scattering in two-level atoms, which occurs in a superradiant way. Our second model is related to the superradiant Rayleigh scattering from a BE condensate. This again leads to a matter-wave amplification but now with the recoiled atoms in the same state as the atoms in the condensate. Here the recoiling atoms are able to interfere with the condensate at rest to form a matter-wave grating (interference fringes ) which is observed experimentally.
We study a highly efficient, matter-wave amplification mechanism in a longitudinally-excited, Bose-Einstein condensate and reveal a very large enhancement due to nonlinear gain from a sixmatter- optical, wave-mixing process involving four photons. Under suitable conditions this opticallydegenerate, four-photon process can be stronger than the usual two-photon inelastic light scattering mechanism, leading to nonlinear growth of the observed matter-wave scattering independent of any enhancement from bosonic stimulation. Our theoretical framework can be extended to encompass even higher-order, nonlinear superradiant processes that result in higher-order momentum transfer.
We investigate theoretically the four-wave mixing of optical and matter waves resulting from the scattering of a short light pulse off an atomic Bose-Einstein condensate, as recently demonstrated by D. Schneble et al. [Science 300, 475 (2003)]]. We show that atomic "pair production" from the condensate results in the generation of both forward- and backward-propagating matter waves. These waves are characterized by different phase-matching conditions, resulting in different angular distributions and temporal evolutions.
The non-equilibrium dynamics of the superradiant scattering of light from a BEC is experimentally investigated by monitoring the time evolution of the population in the condensate. In the experiment, a cigar-shaped Bose-Einstein condensate of /sup 87/Rb atoms is produced and is exposed to a single off-resonant laser pulse directed along the condensate symmetry axis. The superradiant back-scattering of light creates a matter wave pulse moving in the same direction of the laser beam at twice the photon recoil velocity with respect to the original condensate. The efficiency of the process is limited by decoherence between the two atomic spatially overlapped wavepackets. The temporal evolution of the condensate observed in the experiment as well as the results of a simple semiclassical model in which the condensate is described by a density operator for the motional states. The population of the two matter wavepackets as a function of the light pulse duration is reported, together with the experimental points with the analytical formula resulting from the theory of collective atomic recoil laser (CARL).
Recent experiments have demonstrated superradiant Raman scattering from a Bose-Einstein condensate driven by a single off-resonant laser beam. We present a quantum theory describing this phenomenon, showing Raman amplification of matter wave due to collective atomic recoil from 3-level atoms in a $\ensuremath{\Lambda}$-configuration. When atoms are initially in a single lower internal state, a closed two-level system is realized between atoms with different internal states, and entangled atom-photon pairs can be generated. When atoms are initially prepared in both the lower internal states, a fraction of atoms recoiling in the backward direction can be generated.