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arXiv:cond-mat/0701764 · Physical Review A

Ground-state properties of trapped Bose-Einstein condensates: Extension of the Thomas-Fermi approximation

Antonio Muñoz Mateo, V. Delgado

Published Jun 11, 2007• 55 citations
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Abstract

We derive general approximate formulas that provide with remarkable accuracy the ground-state properties of any mean-field scalar Bose-Einstein condensate with short-range repulsive interatomic interactions, confined in arbitrary cylindrically symmetric harmonic traps. Our formulation is even applicable for condensates containing a multiply quantized axisymmetric vortex. We have checked the validity of our formulas by numerically solving the three-dimensional Gross-Pitaevskii equation.

DOI
10.1103/physreva.75.063610

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We derive general approximate formulas that provide with remarkable accuracy the ground-state properties of any mean-field scalar Bose-Einstein condensate with short-range repulsive interatomic interactions, confined in arbitrary cylindrically symmetric harmonic traps. Our formulation is even applicable for condensates containing a multiply quantized axisymmetric vortex. We have checked the validity of our formulas by numerically solving the three-dimensional Gross-Pitaevskii equation.
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-one-dimensional (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.
Abstract We study the mean-field phase-space distribution of the ground state of an anisotropic, harmonically trapped Bose–Einstein condensate at zero temperature. First, we derive the Fourier transform of the ground-state wave function in the Thomas–Fermi limit in d dimensions. Second, we obtain analytical approximations for the Thomas–Fermi Wigner function in one and three dimensions with a factorization ansatz of the coherence function. These approximate expressions are compared with exact numerical simulations of the Gross–Pitaevskii equation.
In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.
In this paper, we present a theoretical study of a Bose–Einstein condensate of interacting bosons in a quartic trap in one-, two- and three-dimensions. Using Thomas–Fermi approximation, suitably complemented by numerical solutions of the Gross–Pitaevskii equation, we study the ground-state condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic confinement.