Stability of a Vortex in a Trapped Bose-Einstein Condensate

TL;DR

This paper analyzes the stability and dynamics of vortices in trapped Bose-Einstein condensates using asymptotic and variational methods, revealing conditions for vortex stability and precession behavior.

Contribution

It provides a detailed analytical study of vortex stability in Bose-Einstein condensates, including conditions for metastability in rotating traps.

Findings

Vortices have unstable modes with positive normalization and negative frequency.

Vortex precession occurs around the trap center.

Vortex stability depends on the trap's angular velocity, with metastability above a critical rotation speed.

Abstract

Based on the method of matched asymptotic expansion and on a time-dependent variational analysis, we study the dynamics of a vortex in the large-condensate (Thomas-Fermi) limit. Both methods as well as an analytical solution of the Bogoliubov equations show that a vortex in a trapped Bose-Einstein condensate has formally unstable normal mode(s) with positive normalization and negative frequency, corresponding to a precession of the vortex line around the center of the trap. In a rotating trap, the solution becomes stable above an angular velocity $\Omega_m$ characterizing the onset of metastability with respect to small transverse displacements of the vortex from the central axis.