Dynamics of a vortex in a trapped Bose-Einstein condensate - art. no. 063617

We consider a large condensate in a rotating anisotropic harmonic trap. Usi ng the method of matched asymptotic expansions, we derive the velocity of a n element of a vortex line as a function of the local gradient of the trap potential, the line curvature, and the angular velocity of the trap rotatio n. This velocity yields small-amplitude normal modes of the vortex for two- dimensional (2D) and 3D condensates. For an axisymmetric trap, the motion o f the vortex line is a superposition of plane-polarized standing-wave modes . In a 2D condensate, the planar normal modes are degenerate, and their sup erposition can result in helical traveling np waves, which differs from a 3 D condensate. Including the effects of trap rotation allows us to find the angular velocity that makes the vortex locally stable. For a cigar-shaped c ondensate, the vortex curvature makes a significant contribution to the fre quency of the lowest unstable normal mode; furthermore, additional modes wi th negative frequencies appear. As a result, it is considerably more diffic ult to stabilize a central vortex in a cigar-shaped condensate than in a di sk-shaped one. Normal modes with imaginary frequencies can occur for a nona xisymmetric condensate (in both 2D and 3D). In connection with recent JILA experiments, we consider the motion of a straight vortex line in a slightly nonspherical condensate. The vortex line changes its orientation in space at the rate proportional to the degree of trap anisotropy and can exhibit p eriodic recurrences.