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arXiv:cond-mat/0107298 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Collapse of attractive Bose-Einstein condensed vortex states in a cylindrical trap

Sadhan K. Adhikari

Published Dec 18, 2001• 68 citations
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Abstract

The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed traps with the larger frequency along either the radial or the axial direction. The critical number of atoms for collapse is calculated as a function of the vortex quantum number L. The critical number increases with increasing angular momentum L of the vortex state but tends to saturate for large L.

DOI
10.1103/physreve.65.016703

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Using the time-dependent mean-field Gross-Pitaevskii equation we study the dynamics of small repulsive Bose-Einstein condensed vortex states of 85Rb{}^{85}\mathrm{Rb}85Rb atoms in a cylindrical trap with low angular momentum $\ensuremath{\Elzxh}L$ per atom (L< 6),(L<~6),(L< 6), when the atomic interaction is suddenly turned attractive by manipulating the external magnetic field near a Feshbach resonance. Consequently, the condensate collapses and ejects atoms via explosion and a remnant condensate with a smaller number of atoms emerges that survives for a long time. Details of this collapse and explosion are compared critically with a similar experiment performed with zero angular momentum (L=0)(L=0)(L=0) by Donley et al. [Nature (London) 412, 295 (2001)]. A suggestion for a future experiment with the vortex state is made.
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The recent Bose-Einstein condensation of ultracold atoms with attractive interactions led us to consider the possibility of probing the stability of its ground state in arbitrary three-dimensional harmonic traps. We performed a quantitative analysis of the critical number of atoms through a full numerical solution of the mean-field Gross-Pitaevskii equation. Characteristic limits are obtained for reductions from three to two and one dimensions, in perfect cylindrical symmetries as well as in deformed ones.
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