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arXiv:0804.4592 · Physical Review A

Stability of excited states of a Bose-Einstein condensate in an anharmonic trap

Dmitry A. Zezyulin, Georgy Leonidovich Alfimov, V. V. Konotop, Víctor M. Pérez‐García

Published Jul 3, 2008• 43 citations
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Abstract

We analyze the stability of nonground nonlinear states of a Bose-Einstein condensate in the mean-field limit in effectively one-dimensional (``cigar-shape'') traps for various types of confining potentials. We find that nonlinear states become, in general, more stable when switching from a harmonic potential to an anharmonic one. We discuss the relation between this fact and the specifics of the harmonic potential which has an equidistant spectrum.

DOI
10.1103/physreva.78.013606

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We analyze the stability of nonground nonlinear states of a Bose-Einstein condensate in the mean-field limit in effectively one-dimensional (``cigar-shape'') traps for various types of confining potentials. We find that nonlinear states become, in general, more stable when switching from a harmonic potential to an anharmonic one. We discuss the relation between this fact and the specifics of the harmonic potential which has an equidistant spectrum.
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We study the stability of Bose-Einstein condensate (BEC) with repulsive and attractive interatomic interactions in a harmonic plus quartic trap $[V(r)=\frac{1}{2}m{\ensuremath{\omega}}^{2}{r}^{2}+\ensuremath{\lambda}{r}^{4}]$. We find that BEC with repulsive interaction becomes more stable for $\ensuremath{\lambda}>0$. For $\ensuremath{\lambda}<0$, we observe a different metastability of the condensate even when the scattering length is positive. For BEC with attractive interaction, we observe dramatic change in the stability factor Acr∣asc∣aho\frac{{A}_{\text{cr}}|{a}_{\text{sc}}|}{{a}_{\text{ho}}}aho​Acr​∣asc​∣​ due to the anharmonicity. The frequencies of the collective excitations are also modified by the atomic interaction and by the anharmonicity.
The dynamics of weakly interacting three-dimensional Bose-Einstein condensates (BECs), trapped in external axially symmetric plus anharmonic distortion potential are studied. Within a variational approach and time-dependent Gross-Pitaevskii equation, the coupled condensate width equations are derived. By modulating anharmonic distortion of the trapping potential, nonlinear features are studied numerically and illustrated analytically, such as mode coupling of oscillation modes, and resonances. Furthermore, the stability of attractive interaction BEC in both repulsive and attractive anharmonic distortion is examined. We demonstrate that a small repulsive and attractive anharmonic distortion is effective in reducing (extending) the condensate stability region since it decreases (increases) the critical number of atoms in the trapping potential.
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The stability and collective excitation of Bose–Einstein condensates with both two- and three-body interactions in a two-dimensional anharmonic trap (i.e., harmonic plus quartic trap) are investigated. By using the variational method, the influence of the three-body interaction and the anharmonicity on the stability are discussed in detail. It is found that the anharmonicity of the trap and the three-body interaction have significant effect on the stability and collective excitations of the system.