Vortex Dynamics Near the Surface of a Bose-Einstein Condensate

TL;DR

This paper analyzes the behavior of vortices near the surface of a Bose-Einstein condensate using both analytical variational methods and numerical solutions of the Gross-Pitaevskii equation, revealing their motion and oscillation characteristics.

Contribution

It provides a new analytical expression for vortex velocity near the surface and combines it with numerical validation, advancing understanding of vortex dynamics in BECs.

Findings

Vortex moves parallel to the surface with constant velocity.

Velocity depends on the vortex's distance from the surface.

Vortex oscillates normal to the surface around a potential minimum.

Abstract

The center-of-mass dynamics of a vortex in the surface region of a Bose-Einstein condensate is investigated both analytically using a variational calculation and numerically by solving the time-dependent Gross-Pitaevskii equation. We find, in agreement with previous works, that away from the Thomas-Fermi surface, the vortex moves parallel to the surface of the condensate with a constant velocity. We obtain an expression for this velocity in terms of the distance of the vortex core from the Thomas-Fermi surface that fits accurately with the numerical results. We find also that, coupled to its motion parallel to the surface, the vortex oscillates along the direction normal to the surface around a minimum point of an effective potential.