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Physical Review A

Bose-Einstein condensation in an external potential

Vanderlei Salvador Bagnato, David E. Pritchard, Daniel Kleppner

Published May 1, 1987• 435 citations
Publisher

Abstract

We present theoretical results for the critical temperature for Bose-Einstein condensation, condensate fraction, and heat capacity of a gas of Bose particles that are confined by a generic power-law potential trap. All three of these quantities are found to vary markedly with the shape of the potential. Both the ideal and the weakly interacting Bose gas are considered.

DOI
10.1103/physreva.35.4354

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We present theoretical results for the critical temperature for Bose-Einstein condensation, condensate fraction, and heat capacity of a gas of Bose particles that are confined by a generic power-law potential trap. All three of these quantities are found to vary markedly with the shape of the potential. Both the ideal and the weakly interacting Bose gas are considered.
The critical temperature for Bose-Einstein condensation, ground-state fraction, and heat capacity of an ideal gas of Bose particles that are confined by an n-dimensional generic power-law potential trap are derived. The conditions for Bose-Einstein condensation and the discontinuous conditions of the heat capacity at critical temperature are obtained. All these quantities and conditions are found to vary markedly with the dimensionality of space, characteristics of particles, and shape of the external potential. The results obtained here are universal.
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Thermodynamic properties of ideal Bose gas trapped in an external generic power law potential are investigated systematically from the grand thermodynamic potential in ddd dimensional space. The most general conditions for Bose-Einstein condensate and the discontinuous conditions of heat capacity at the critical temperature in presence of generic power law potential are presented in this manuscript. The dependence of the physical quantities on external potential, particle characteristics and space dimensionality are discussed. The more general results obtained in this paper presents an unified illustration of Bose-Einstein condensation of ideal Bose systems as they reduces to the expressions and conclusions available in the literature with appropiate choice of power law exponent.
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.
The properties of a trapped ideal Bose gas in n -dimensional space are studied. General analytic expressions of the critical temperature of Bose-Einstein condensation, the jump of heat capacity at and the fraction of condensation at temperatures below have been derived. How these physical quantities depend on the external potential, particle characteristics and space dimensionality are discussed. We find that when a proper external potential is taken, Bose-Einstein condensation may occur in any dimensional space.