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arXiv:cond-mat/0106208 · Journal of Physics B Atomic Molecular and Optical Physics

Critical temperature and condensate fraction of the trapped interacting Bose gas with finite-size effects

Hongwei Xiong, Shujuan Liu, Guoxiang Huang, Xu Zhi-Jun, Cunyuan Zhang

Published Jul 19, 2001• 15 citations
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Abstract

The critical temperature and condensate fraction of a trapped interacting Bose gas are investigated when both atom-atom interaction and finite-size effects are taken into account. A canonical ensemble is used to obtain the equations on the condensate fraction for the trapped interacting Bose gas near and below the critical temperature. In our approaches corrections due to atom-atom interaction and finite-size effects are obtained simultaneously for the critical temperature and condensate fraction of the system. An analytical high-order correction to the condensate fraction is given.

DOI
10.1088/0953-4075/34/15/308

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We investigate the interaction effect between atoms and the finite size effect of a Bose-Einstein gas at finite temperature. Using a mean field approach, we derive the thermodynamic potential on finite systems and obtain the condensate fraction, the chemical potential and the internal energy with the interaction and the finite size effects taken into account. In this approach, we can treat thermodynamic quantities as those of the ideal Bose gas. It is found that the interaction effect shifts the transition temperature by a few percent toward the lower temperature. Above the transition temperature, these quantities agree with the noninteracting Bose gas.
We investigate theoretically Bose-Einstein condensation of an ideal, trapped Bose gas in the presence of Rashba spin-orbit coupling. Analytic results for the critical temperature and condensate fraction are derived based on a semiclassical approximation to the single-particle-energy spectrum and density of states and are compared with exact results obtained by explicitly summing discrete energy levels for a small number of particles. We find a significant decrease of the critical temperature and of the condensate fraction due to finite spin-orbit coupling. For a large coupling strength and a finite number of particles NNN, the critical temperature scales as N2/5{N}^{2/5}N2/5 and N2/3{N}^{2/3}N2/3 in three and two dimensions, respectively, contrasted to the predictions of N1/3{N}^{1/3}N1/3 and N1/2{N}^{1/2}N1/2 in the absence of spin-orbit coupling. Finite-size corrections in three dimensions are also discussed.