Extension of the Thomas-Fermi approximation for trapped Bose-Einstein condensates with an arbitrary number of atoms

Details Extension of the Thomas-Fermi approximation for trapped Bose-Einstein condensates with an arbitrary number of atoms Extension of the Thomas-Fermi approximation for trapped Bose-Einstein condensates with an arbitrary number of atoms

2007-01-29

arxiv.org/abs/cond-mat/0701695v1

Phys. Rev. A 74, 065602 (2006)

Physics

Condensed Matter

Other Condensed Matter

5 pages, 3 figures. Final version published in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.74.065602

By incorporating the zero-point energy contribution we derive simple and accurate extensions of the usual Thomas-Fermi (TF) expressions for the ground-state properties of trapped Bose-Einstein condensates that remain valid for an arbitrary number of atoms in the mean-field regime. Specifically, we obtain approximate analytical expressions for the ground-state properties of spherical, cigar-shaped, and disk-shaped condensates that reduce to the correct analytical formulas in both the TF and the perturbative regimes, and remain valid and accurate in between these two limiting cases. Mean-field quasi-1D and -2D condensates appear as simple particular cases of our formulation. The validity of our results is corroborated by an independent numerical computation based on the 3D Gross-Pitaevskii equation.

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