Landau levels and the Thomas-Fermi structure of rapidly rotating Bose-Einstein condensates

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  • 30 March 2004
Abstract
We show that the density profile of a rapidly rotating harmonically trapped Bose-Einstein condensate will be of the Thomas-Fermi inverted parabolic form as long as the number of vortices is much larger than unity. Two forms of the condensate wave function are explored: in the first we multiply the lowest Landau level (LLL) wave function with a regular lattice of vortices by a slowly varying envelope function, which gives rise to components in higher Landau levels; in the second we retain the LLL form of the condensate but relax the requirement that the vortices lie on a regular lattice. Performing variational calculations for the two cases, we find it most favorable energetically to retain the LLL form of the wave function but to allow the vortices to deviate slightly from a regular lattice. Marked changes in the density profile are, as we see, accompanied by reduction in the energy of only several percent.

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