Vortex precession and exchange in a Bose-Einstein condensate

TL;DR

This paper models vortex dynamics in Bose-Einstein condensates using the Gross-Pitaevskii equation, revealing how vortex precession and phase shifts depend on angular momentum and how vortex pairs interact via an emergent gauge field.

Contribution

It introduces a method to analyze vortex precession and phase dynamics in BECs, highlighting the role of angular momentum and emergent gauge fields in vortex interactions.

Findings

Vortex core precesses around trap center with velocity depending on angular momentum.

Phase of vortex wave function shifts at a constant rate related to precession.

Vortex pairs exhibit gauge field interactions with flux proportional to their velocities.

Abstract

Vortices in a Bose-Einstein condensate are modelled as spontaneously symmetry breaking minimum energy solutions of the time dependent Gross-Pitaevskii equation, using the method of constrained optimization. In a non-rotating axially symmetric trap, the core of a single vortex precesses around the trap center and, at the same time, the phase of its wave function shifts at a constant rate. The precession velocity, the speed of phase shift, and the distance between the vortex core and the trap center, depend continuously on the value of the conserved angular momentum that is carried by the entire condensate. In the case of a symmetric pair of identical vortices, the precession engages an emergent gauge field in their relative coordinate, with a flux that is equal to the ratio between the precession and shift velocities.