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arXiv:1403.1474

Bose-Einstein condensates in multiple well potentials from a variational path integral

Wattana Ratismith, Holger Hauptmann, Walter T. Strunz

Published Mar 6, 2014• 0 citations
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Abstract

We apply a path integral variational approach to obtain analytical expressions for condensate wave functions of an ultracold, interacting trapped Bose gases. As in many recent experiments, the particles are confined in a 1D or 3D harmonic oscillator trap which is superimposed by a periodic potential in one direction. Based on the first order cumulant expansion with respect to a harmonic trial action, and emplyoing a mean-field approximation, optimal variational parameters are obtained by minimizing an analytical expression for the ground state energy. Our largely analytical results for energy and condensate wave function are in good agreement with fully numerical calculations based on the Gross-Pitaevskii equation.

DOI
10.48550/arxiv.1403.1474

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In this paper, we discuss theoretically the behavior of ideal Bose-Einstein gases in a 3D box and in a harmonic trap. We make use of the mean filed theory based on the time dependent Gross-Pitaevskii equation which describes the main features of Bose-Einstein condensation. We investigate and discuss the density profiles and the ground state properties of a trapped condensate confined in harmonic trap. We found out that in an attractive interaction, the gas tends to increase its central density in order to lower the interaction energy.