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Journal of Modern Optics

Response of trapped Bose-Einstein condensates under time-dependent perturbation

Tomoi Koide C, M. Mine, Masahiko Okumura, Y. Yamanaka

Published Apr 1, 2004• 1 citation
Publisher
DOI
10.1080/09500340408233641

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The response of a trapped Bose-Einstein condensed gas to a density perturbation generated by a two-photon Bragg pulse is investigated by solving the time-dependent Gross-Pitaevskii equation. We calculate the total momentum imparted to the condensate as a function of both the time duration of the pulse and the frequency difference of the two laser beams. The role of the dynamic response function in characterizing the time evolution of the system is pointed out, with special emphasis to the phonon regime. Numerical simulations are compared with the predictions of local-density approximation. The relevance of our results for the interpretation of current experiments is also discussed.
We investigate the response of a Bose-Einstein condensate of trapped, neutral atoms to weak and strong sinusoidal perturbation of the trapping potential both by solving the Bogoliubov equations and by direct integration of the time-dependent, driven Ginzburg-Pitaevskii-Gross equation. We find that the distortion of the condensate is maximal when the frequency of the perturbation equals one of the mode positions of the condensate's excitation spectrum. On resonance, the condensate exhibits a strong nonlinear response that can be used as a clear signature of the mode frequency in an experiment where the trap potential is weakly perturbed. For strong driving, we find evidence for an array of nonlinear effects such as harmonic generation and frequency mixing. These phenomena are the matter-wave analogs of conventional nonlinear optics and should be straightforward to study in evaporatively cooled samples of alkali-metal atoms. \textcopyright{} 1996 The American Physical Society.
We present a comprehensive theoretical study of vortex lattice formation in atomic Bose-Einstein condensates confined by a rotating elliptical trap. We consider rotating solutions of the classical hydrodynamic equations and their response to perturbations, as well as time-dependent simulations. We discriminate three distinct, experimentally testable, regimes of instability: ripple, interbranch, and catastrophic. Under symmetry-breaking perturbations these instabilities lead to lattice formation even at zero temperature. While our results are consistent with previous theoretical and experimental results, they shed further light on lattice formation.