Nucleation and kinematics of vortices in stirred Bose Einstein condensates

TL;DR

This paper uses a formalism within the Gross-Pitaevskii theory to analyze how vortices form and move in a stirred two-dimensional Bose-Einstein condensate, revealing the conditions for vortex nucleation.

Contribution

It introduces a defect density field to study vortex nucleation and demonstrates the formalism's effectiveness in deriving vortex dynamics from the Gross-Pitaevskii equation.

Findings

Phase slips occur inside hard potentials without vortex nucleation.

Vortex nucleation in soft potentials requires a critical stirring velocity.

The formalism accurately derives vortex dynamics from the Gross-Pitaevskii equation.

Abstract

We apply the Halperin-Mazenco formalism within the Gross-Pitaevskii theory to characterise the kinematics and nucleation of quantum vortices in a two-dimensional stirred Bose Einstein condensate. We introduce a smooth defect density field measuring the superfluid vorticity and is a topologically conserved quantity. We use this defect density field and its associated current density to study the precursory pattern formations that occur inside the repulsive potential of an obstacle and determine the onset of vortex nucleation and shedding. We demonstrate that phase slips form inside hard potentials even in the absence of vortex nucleation, whereas for soft potentials they occur only above a critical stirring velocity leading to vortex nucleation. The Halperin-Mazenco formalism provides an elegant and accurate method of deriving the point vortex dynamic directly from the Gross-Pitaevskii equation.