Distributed vorticity model for vortex molecule dynamics

TL;DR

This paper develops an improved theoretical model for vortex molecule dynamics in two-component Bose-Einstein condensates near a hard wall, incorporating a continuous distribution of image vorticity, and validates it with numerical simulations.

Contribution

It extends previous models by including a continuous image vorticity distribution to better capture vortex molecule interactions with boundaries.

Findings

The continuous vorticity distribution weakens the vortex precession frequency.

The model's predictions align well with numerical simulations.

Improved understanding of vortex-boundary interactions in BECs.

Abstract

We analyze the effect of a hard wall trapping potential on the dynamics of a vortex molecule in a two-component Bose-Einstein condensate with linear coherent coupling. A vortex molecule consists of a vortex of the same charge in each component condensate connected by a domain wall of the relative phase. In a previous paper Ref.[Phys. RevA. 106,043319(2022)] we described the interaction of a vortex molecule with the boundary using the method of images by separately treating each component vortex as a point vortex, in addition to a Magnus force effect from the surface tension of the domain wall. Here we extend the model by considering a continuous distribution of image vorticity reflecting the effect of the domain wall on the vortex molecule phase structure. In the case of a precessing centered vortex molecule in an isotropic trap, distributing the image vorticity weakens its contribution to the precession frequency. We test the model predictions against numerical simulations of the coupled Gross-Pitaevskii equations in a two-dimensional circular disc and find support for the improved model.