Dynamics of a Vortex in a Trapped Bose-Einstein Condensate

TL;DR

This paper analyzes vortex dynamics in rotating Bose-Einstein condensates using asymptotic methods, revealing how trap shape and rotation influence vortex stability, normal modes, and vortex line motion.

Contribution

It derives vortex velocity and normal modes in anisotropic traps, including effects of rotation and shape, providing new insights into vortex stability and dynamics in BECs.

Findings

Vortex velocity depends on trap potential gradient, curvature, and rotation.

Normal modes include standing waves and helical traveling waves.

Cigar-shaped condensates have more unstable modes and are harder to stabilize.

Abstract

We consider a large condensate in a rotating anisotropic harmonic trap. Using the method of matched asymptotic expansions, we derive the velocity of an element of vortex line as a function of the local gradient of the trap potential, the line curvature and the angular velocity of the trap rotation. This velocity yields small-amplitude normal modes of the vortex for 2D and 3D condensates. For an axisymmetric trap, the motion of the vortex line is a superposition of plane-polarized standing-wave modes. In a 2D condensate, the planar normal modes are degenerate, and their superposition can result in helical traveling waves, which differs from a 3D condensate. Including the effects of trap rotation allows us to find the angular velocity that makes the vortex locally stable. For a cigar-shape condensate, the vortex curvature makes a significant contribution to the frequency of the lowest unstable normal mode; furthermore, additional modes with negative frequencies appear. As a result, it is considerably more difficult to stabilize a central vortex in a cigar-shape condensate than in a disc-shape one. Normal modes with imaginary frequencies can occur for a nonaxisymmetric 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 periodic recurrences.