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arXiv:cond-mat/0607619 · Physical Review A

Bose-Einstein-condensed atoms in toroidal traps

Andrew David Jackson, G. M. Kavoulakis

Published Dec 15, 2006• 20 citations
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Abstract

We consider Bose-Einstein-condensed atoms confined in a toroidal trap. Under conditions of one-dimensional behavior, the density distribution of the atoms may be exponentially localized or delocalized, even for very small variations in the trapping potential along the torus. For similar reasons, small irregularities of the trap may also have a very pronounced effect on the density of the cloud. The excitation spectrum is also affected by the presence of some spatially varying potential and/or irregularities in the trap.

DOI
10.1103/physreva.74.065601

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We consider Bose-Einstein-condensed atoms confined in a toroidal trap. Under conditions of one-dimensional behavior, the density distribution of the atoms may be exponentially localized or delocalized, even for very small variations in the trapping potential along the torus. For similar reasons, small irregularities of the trap may also have a very pronounced effect on the density of the cloud. The excitation spectrum is also affected by the presence of some spatially varying potential and/or irregularities in the trap.
Motivated by numerous experiments on Bose-Einstein condensed atoms which have been performed in tight trapping potentials of various geometries [elongated and/or toroidal (annular)], we develop a general method which allows us to reduce the corresponding three-dimensional Gross-Pitaevskii equation for the order parameter into an effectively one-dimensional equation, taking into account the interactions (i.e., treating the width of the transverse profile variationally) and the curvature of the trapping potential. As an application of our model we consider atoms which rotate in a toroidal trapping potential. We evaluate the state of lowest energy for a fixed value of the angular momentum within various approximations of the effectively one-dimensional model and compare our results with the full solution of the three-dimensional problem, thus getting evidence for the accuracy of our model.
We discuss thermal and dynamical properties of Bose condensates confined by an external potential. First we analyze the Bose-Einstein transition temperature for an ideal Bose gas in a generic power-law potential and d-dimensional space. Then we investigate the effect of the shape of the trapping potential on the properties of a weakly-interacting Bose condensate. We show that using exotic trapping potentials the condensate can exhibit interesting coherent quantum phenomena, like superfluidity and tunneling. In particular, we consider toroidal and double-well potentials. The theoretical results are compared with recent experiments.