Dynamics of a massive superfluid vortex in $r^k$ confining potentials

TL;DR

This paper models the motion of superfluid vortices in various $r^k$ confining potentials, revealing how vortex precession and dynamics depend on core mass and potential shape, with implications for experimental realizations.

Contribution

It introduces a unified effective point-vortex model for superfluid vortices in power-law traps, including core mass effects, and analyzes their dynamics and precession behavior.

Findings

Vortex precession direction can reverse with increasing core mass.

Effective potential $V_{eff}$ often has a single minimum leading to uniform precession.

The model applies to experimentally realizable optical-trapping scenarios.

Abstract

We study the motion of a superfluid vortex in condensates having different background density profiles, ranging from parabolic to uniform. The resulting effective point-vortex model for a generic power-law potential $\propto r^k$ can be experimentally realized with recent advances in optical-trapping techniques. Our analysis encompasses both empty-core and filled-core vortices. In the latter case, the vortex acquires a mass due to the presence of distinguishable atoms located in its core. The axisymmetry allows us to reduce the coupled dynamical equations of motion to a single radial equation with an effective potential $V_{\rm eff}$. In many cases, $V_{\rm eff}$ has a single minimum, where the vortex precesses uniformly. The dynamics of the vortex and the localized massive core arises from the dependence of the energy on the radial position of the vortex and from the $r^k$ trap potential. We find that a positive vortex with small mass orbits in the positive direction, but the sense of precession can reverse as the core mass increases. Early experiments and theoretical studies on two-component vortices found some qualitatively similar behavior.