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arXiv:cond-mat/0001163 · Physical Review A

Analytical estimate of the critical velocity for vortex pair creation in trapped Bose condensates

Michael Crescimanno, C. G. Koay, R. Peterson, R. L. Walsworth

Published Nov 15, 2000• 28 citations
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Abstract

We use a Thomas-Fermi approximation that includes the leading kinetic terms due to fluid motion to estimate analytically the critical velocity for the formation of vortex pairs in harmonically trapped Bose-Einstein condensates. We find rough agreement between this analytical estimate and recent experiments on trapped sodium gas condensates.

DOI
10.1103/physreva.62.063612

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We use a Thomas-Fermi approximation that includes the leading kinetic terms due to fluid motion to estimate analytically the critical velocity for the formation of vortex pairs in harmonically trapped Bose-Einstein condensates. We find rough agreement between this analytical estimate and recent experiments on trapped sodium gas condensates.
A relaxation method is employed to study a rotating dense Bose-Einstein condensate beyond the Thomas-Fermi approximation. We use a slave-boson model to describe the strongly interacting condensate and derive a generalized nonlinear Schr\"odinger equation with a kinetic term for the rotating condensate. In comparison with previous calculations, based on the Thomas-Fermi approximation, significant improvements are found in regions where the condensate in a trap potential is not smooth. The critical angular velocity of the vortex formation is higher than in the Thomas-Fermi prediction.
We consider the leading corrections to the Thomas-Fermi approach to the description of the properties of a magnetically trapped, Bose-condensed cloud of atoms. Simple analytical expressions are derived for the kinetic energy in terms of an effective cutoff length, which we calculate numerically by considering the one-dimensional problem for a linear-ramp potential. We also determine the lowest angular velocity at which it is energetically favorable for a vortex to enter the cloud. For large clouds, our results are in excellent agreement with available numerical calculations.
We present an analytical approximation for nonlinear dynamics of trapped Bose-Einstein condensates. The approximation is a substantial improvement over the Thomas-Fermi approximation and is shown to be applicable for systems with a rather small number of atoms N. The calculated aspect ratios after ballistic expansion are found to be in good agreement with those observed in recent experiments. The approximation is useful in providing a simple and easy quantitative computational tool for the analysis of experimental data.