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Physical Review A

Chemical potential of a trapped interacting Bose gas

Zhuyue Zhang, Haixiang Fu, Jincan Chen, Mingzhe Li

Published May 27, 2009• 4 citations
Publisher

Abstract

A Bose gas with repulsive interactions in a generic power-law potential is studied in the Hartree-Fock approximation. The scaling parameter characterizing the role of two-body repulsive interactions is expressed in terms of the scaled scattering length and the trap parameter. The chemical potential obtained here provides a correction to the existing analytical result, especially in the critical region of Bose-Einstein condensation.

DOI
10.1103/physreva.79.055603

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A Bose gas with repulsive interactions in a generic power-law potential is studied in the Hartree-Fock approximation. The scaling parameter characterizing the role of two-body repulsive interactions is expressed in terms of the scaled scattering length and the trap parameter. The chemical potential obtained here provides a correction to the existing analytical result, especially in the critical region of Bose-Einstein condensation.
We investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number NNN of atoms, harmonic oscillator length, deformation of the trap, sss-wave scattering length) fix its thermodynamic behavior in the large NNN limit through two dimensionless scaling parameters. These are the reduced temperature t=T/Tc0t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T/{T}_{c}^{0}t=T/Tc0​ and the ratio $\ensuremath{\eta}$ between the T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature Tc0{T}_{c}^{0}Tc0​ of the noninteracting model. The scaling functions relative to the condensate fraction, energy, chemical potential, and moment of inertia are calculated within the Popov approximation.
We devote a particular attention to the role played by the repulsive interaction on the chemical potential of condensed atoms, the chemical potential of non-condensed atoms, the anomalous fraction and the heat specific capacity for Bose gas in harmonic trap. First, we point out that the generalized Hartree-Fock Bogoliubov approximations (GHFB) produces a change in the specific temperature via estimation experience, and we discuss these inadequacies. We calculate a behavior of condensate density in Thomas Fermi approximation, where the thermal cloud is not negligible. Finally, we compare our results with various recent numerical estimates and experience.
We investigate the critical temperature of an interacting Bose gas confined in a trap described by a generic isotropic power-law potential. We compare the results with respect to the non-interacting case. In particular, we derive an analytical formula for the shift of the critical temperature holding to first order in the scattering length. We show that this shift scales as Nn/3(n+2), where N is the number of Bosons and n is the exponent of the power-law potential. Moreover, the sign of the shift critically depends on the power-law exponent n. Finally, we find that the shift of the critical temperature due to finite-size effects vanishes as N-2n/3(n+2).