Motion of vortices in inhomogeneous Bose-Einstein condensates

TL;DR

This paper derives an exact equation for vortex motion in inhomogeneous Bose-Einstein condensates, validated by simulations, revealing the significant role of phase gradients over density gradients in certain traps.

Contribution

It introduces a novel analytical vortex velocity formula incorporating both density and phase effects, enhancing modeling accuracy in inhomogeneous condensates.

Findings

Vortex velocity is mainly influenced by ambient phase gradients in harmonic traps.

The derived point-vortex model accounts for both density and phase contributions.

Simulations show complex effects of nonuniform density are challenging to model simply.

Abstract

We derive a general and exact equation of motion for a quantised vortex in an inhomogeneous two-dimensional Bose-Einstein condensate. This equation expresses the velocity of a vortex as a sum of local ambient density and phase gradients in the vicinity of the vortex. We perform Gross-Pitaevskii simulations of single vortex dynamics in both harmonic and hard-walled disk-shaped traps, and find excellent agreement in both cases with our analytical prediction. The simulations reveal that, in a harmonic trap, the main contribution to the vortex velocity is an induced ambient phase gradient, a finding that contradicts the commonly quoted result that the local density gradient is the only relevant effect in this scenario. We use our analytical vortex velocity formula to derive a point-vortex model that accounts for both density and phase contributions to the vortex velocity, suitable for use in inhomogeneous condensates. Although good agreement is obtained between Gross-Pitaevskii and point-vortex simulations for specific few-vortex configurations, the effects of nonuniform condensate density are in general highly nontrivial, and are thus difficult to efficiently and accurately model using a simplified point-vortex description.