Hydrodynamic Approach to Vortex Lifetime in Trapped Bose Condensates

TL;DR

This paper models vortex dynamics in trapped Bose-Einstein condensates at zero temperature, deriving effective potentials and estimating vortex lifetimes considering trap imperfections, with implications for understanding vortex stability and decay.

Contribution

It introduces a variational approach to calculate the effective potential and precession frequency of vortices in trapped condensates, and estimates vortex lifetime considering trap imperfections.

Findings

Vortex precession frequency is lower than elementary excitation frequencies.

Off-center vortices follow circular trajectories around the trap center.

Trap imperfections influence vortex lifetime estimates.

Abstract

We study a vortex in a two-dimensional, harmonically trapped Bose-Einstein condensate at zero temperature. Through a variational calculation using a trial condensate wave function and a nonlinear Schroedinger Lagrangian, we obtain the effective potential experienced by a vortex at an arbitrary position in the condensate, and find that an off-center vortex will move in a circular trajectory around the trap center. We find the frequency of this precession to be smaller than the elementary excitation frequencies in the cloud. We also study the radiation of sound from a moving vortex in an infinite, uniform system, and discuss the validity of this as an approximation for the trapped case. Furthermore, we estimate the lifetime of a vortex due to imperfections in the trapping potential.