A vortex dipole in a trapped two-dimensional Bose-Einstein condensate

TL;DR

This paper investigates the behavior and stationary states of vortex-antivortex pairs in a 2D Bose-Einstein condensate, combining analytical, numerical, and exact solutions to understand vortex dynamics in trapped systems.

Contribution

It introduces a comprehensive framework for analyzing vortex-antivortex configurations in trapped BECs using variational, numerical, and exact methods.

Findings

Characterization of stationary vortex-antivortex states

Identification of bifurcation points for soliton-like solutions

Insights into vortex motion mechanisms in harmonic traps

Abstract

We study the conservative dynamics and stationary configurations of a vortex-antivortex pair in a harmonically trapped two-dimensional Bose-Einstein condensate. We establish the conceptual framework for understanding the stationary states and the topological defect trajectories, through considerations of different mechanisms of vortex motion and the bifurcation of soliton-like stationary solutions. Our insights are based on Lagrangian-based variational calculations, numerical solutions of both the time-dependent and time-independent Gross-Pitaevskii equations, and exact solutions for the non-interacting case.