Velocity of vortices in inhomogeneous Bose-Einstein condensates

TL;DR

This paper derives an exact formula for vortex velocity in Bose-Einstein condensates from the Gross-Pitaevskii equation, revealing that vortices can move independently of the local superfluid velocity, especially in rapidly rotating traps.

Contribution

It provides a new exact expression for vortex velocity in inhomogeneous condensates and explores vortex dynamics in various rotation regimes.

Findings

Vortex velocity includes local superfluid velocity plus a density gradient correction.

In rapid rotation, vortices do not follow the local fluid velocity.

Derived an exact wave function for a vortex near the rotation axis.

Abstract

We derive, from the Gross-Pitaevskii equation, an exact expression for the velocity of any vortex in a Bose-Einstein condensate, in equilibrium or not, in terms of the condensate wave function at the center of the vortex. In general, the vortex velocity is a sum of the local superfluid velocity, plus a correction related to the density gradient near the vortex. A consequence is that in rapidly rotating harmonically trapped Bose-Einstein condensates, unlike in the usual situation in slowly rotating condensates and in hydrodynamics, vortices do not move with the local fluid velocity. We indicate how Kelvin's conservation of circulation theorem is compatible with the velocity of the vortex center being different from the local fluid velocity. Finally we derive an exact wave function for a single vortex near the rotation axis in a weakly interacting system, from which we derive the vortex precession rate.