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arXiv:cond-mat/9901121 · Physical Review A

Bosons in a toroidal trap: Ground state and vortices

Luca Salasnich, Alberto Parola, L. Reatto

Published Apr 1, 1999• 48 citations
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Abstract

We study the Bose-Einstein condensate (BEC) in a three-dimensional toroidal sombrero-shaped trap. By changing the parameters of the potential, or the number of bosons, it is possible to modify strongly the density profile of the BEC. We consider the ground-state properties for positive and negative scattering length and calculate the spectrum elementary excitations. We also discuss the macroscopic phase coherence and superfluidity of the BEC by analyzing vortex states and their stability.

DOI
10.1103/physreva.59.2990

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We study a Bose-Einstein condensate of 52Cr^{52}\mathrm{Cr}52Cr atoms confined in a toroidal trap with a variable strength of sss-wave contact interactions. We analyze the effects of the anisotropic nature of the dipolar interaction by considering the magnetization axis to be perpendicular to the trap symmetry axis. In the absence of a central repulsive barrier, when the trap is purely harmonic, the effect of reducing the scattering length is a tuning of the geometry of the system from a pancake-shaped condensate when it is large to a cigar-shaped condensate for small scattering lengths. For a condensate in a toroidal trap, the interaction in combination with the central repulsive Gaussian barrier produces an azimuthal dependence of the particle density for a fixed radial distance. We find that along the magnetization direction the density decreases as the scattering length is reduced but presents two symmetric density peaks in the perpendicular axis. For even lower values of the scattering length we observe that the system undergoes a dipolar-induced symmetry breaking phenomenon. The whole density becomes concentrated in one of the peaks, resembling an origin-displaced cigar-shaped condensate. In this context we also analyze stationary vortex states and their associated velocity fields, finding that these also show a strong azimuthal dependence for small scattering lengths. The expectation value of the angular momentum along the zzz direction provides a qualitative measure of the difference between the velocity in the different density peaks.
We study the Bose-Einstein condensate in the MIT double-well trap. We calculate the ground-state density profile of 23{}^{23}23Na atoms and the Bogoliubov spectrum of the elementary excitations as a function of the strength of the double-well barrier. In particular, we analyze the behavior of quantum-mechanical collective excitations. Finally, we discuss the observability criteria for macroscopic quantum tunneling and macroscopic quantum self-trapping.
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