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arXiv:cond-mat/0405316

Period-doubled breathing in trapped Bose-Einstein condensates

Emil Lundh

Published May 14, 2004• 0 citations
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Abstract

The response of a trapped Bose-Einstein condensed gas to a periodic driving force is studied theoretically in the framework of the nonlinear Gross-Pitaevskii equation. The monopole mode is driven by periodical modulation of the frequency of the isotropic harmonic trapping potential. Period-doubled motion is shown to occur when the driving is strong and close to resonance with the monopole mode. A variational model predicts chaotic oscillations but is found to disagree with the full solutions to the Gross-Pitaevskii equation.

DOI
10.48550/arxiv.cond-mat/0405316

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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.
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A hydrodynamical version of the time-dependent Gross-Pitaevskii equation has been formulated and applied to the description of a Bose-Einstein condensate (BEC) of 87{}^{87}87Rb atoms in the JILA time-averaged orbiting potential (TOP) trap. The response of the BEC to time-dependent modulations of the trap potential is computed and the characteristic frequencies of a BEC oscillation agree well with those observed in recent experiments. For the axially symmetric m=0m=0m=0 mode of the TOP trap, we find a weak dependence of the oscillatory frequency on the strength of the driving amplitude under conditions comparable to those of current experiments. The free ringing of the BEC that is induced by a transient change in the potential is found to be periodic, in agreement with the predictions of Thomas-Fermi theory. We analyze the harmonic content of the spectral response and consider possibilities for high-harmonic generation in the context of nonlinear atom optics.