Vortices in Bose-Einstein-Condensed Atomic Clouds

TL;DR

This paper investigates the dynamics of vortex states in Bose-Einstein condensates at zero temperature using analytical and numerical solutions of the Gross-Pitaevskii equation, providing insights into their expansion and experimental observability.

Contribution

It offers a combined analytical and numerical analysis of vortex dynamics in BECs, including expansion behavior and conditions for experimental detection.

Findings

Cloud radius expands as (1+ω²t²)^{1/2} in 2D

Vortex core and cloud expansion depend on particle number and interactions

Conditions for experimental observation of vortices are discussed

Abstract

The properties of vortex states in a Bose-Einstein condensed cloud of atoms are considered at zero temperature. Using both analytical and numerical methods we solve the time-dependent Gross-Pitaevskii equation for the case when a cloud of atoms containing a vortex is released from a trap. In two dimensions we find the simple result that the time dependence of the cloud radius is given by $(1+\omega^2t^2)^{1/2}$, where $\omega$ is the trap frequency. We calculate and compare the expansion of the vortex core and the cloud radius for different numbers of particles and interaction strengths, in both two and three dimensions, and discuss the circumstances under which vortex states may be observed experimentally.