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arXiv:cond-mat/0105600 · Physical Review A

Localized breathing oscillations of Bose-Einstein condensates in periodic traps

R. Carretero-González, Keith Promislow

Published Sep 20, 2002• 77 citations
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Abstract

We demonstrate the existence of localized oscillatory breathers for quasi-one-dimensional Bose-Einstein condensates confined in periodic potentials. The breathing behavior corresponds to position oscillations of individual condensates about the minima of the potential lattice. We deduce the structural stability of the localized oscillations from the construction. The stability is confirmed numerically for perturbations to the initial state of the condensate, to the potential trap, as well as for external noise. We also construct periodic and chaotic extended oscillations for the chain of condensates. All our findings are verified by direct numerical integration of the Gross-Pitaevskii equation in one dimension.

DOI
10.1103/physreva.66.033610

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We demonstrate the existence of localized oscillatory breathers for quasi-one-dimensional Bose-Einstein condensates confined in periodic potentials. The breathing behavior corresponds to position oscillations of individual condensates about the minima of the potential lattice. We deduce the structural stability of the localized oscillations from the construction. The stability is confirmed numerically for perturbations to the initial state of the condensate, to the potential trap, as well as for external noise. We also construct periodic and chaotic extended oscillations for the chain of condensates. All our findings are verified by direct numerical integration of the Gross-Pitaevskii equation in one dimension.
We consider the interaction of Bose-Einstein condensates in a nonlinear lattice formed from the local minima of an externally imposed periodic potential. Within a one-dimensional geometry, we develop a perturbation expansion for the motion of a condensate within the confines of the local minima of its potential well, coupled to the near-neighbor interaction with the adjacent condensates. We show that the resultant system of lattice differential equations possesses spatially localized breathing solutions.
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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.
We study the nonlinear dynamics of two-component Bose–Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross–Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.