Normal Modes of a Vortex in a Trapped Bose-Einstein Condensate

Details Normal Modes of a Vortex in a Trapped Bose-Einstein Condensate Normal Modes of a Vortex in a Trapped Bose-Einstein Condensate

1998-03-14

arxiv.org/abs/cond-mat/9803181v2

Physics

Condensed Matter

15 pages, REVTEX, 2 Postscript figures, to appear in Phys. Rev. A. We have altered the material in Secs. 3B and 4 in connectio

Scientific paper

10.1103/PhysRevA.58.3168

A hydrodynamic description is used to study the normal modes of a vortex in a zero-temperature Bose-Einstein condensate. In the Thomas-Fermi (TF) limit, the circulating superfluid velocity far from the vortex core provides a small perturbation that splits the originally degenerate normal modes of a vortex-free condensate. The relative frequency shifts are small in all cases considered (they vanish for the lowest dipole mode with |m|=1), suggesting that the vortex is stable. The Bogoliubov equations serve to verify the existence of helical waves, similar to those of a vortex line in an unbounded weakly interacting Bose gas. In the large-condensate (small-core) limit, the condensate wave function reduces to that of a straight vortex in an unbounded condensate; the corresponding Bogoliubov equations have no bound-state solutions that are uniform along the symmetry axis and decay exponentially far from the vortex core.

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