Bose-Einstein Condensation in a Confined Geometry with and without a Vortex

TL;DR

This paper critically examines mean-field theories for dilute Bose gases in confined geometries, analyzing condensate structures, excitation spectra, and vortex behavior through numerical solutions within the Bogoliubov approximation.

Contribution

It provides a detailed numerical analysis of condensate and vortex properties in confined geometries, comparing various mean-field theories with new predictions.

Findings

Spatial structures of condensate and non-condensate components identified

Excitation spectra and local density of states characterized

Circulating current densities in vortices predicted

Abstract

Various widely-used mean-field type theories for a dilute Bose gas are critically examined in the light of the recent discovery of Bose-Einstein condensation of atomic gases in a confined geometry. By numerically solving the mean-field equations within the framework of the Bogoliubov approximation both stationary non-uniform case and the vortex case under rotation in a cylindrically symmetric vessel are investigated. We obtain spatial structures of condensate, non-condensate, anomalous correlation. The low lying excitation spectra, the local density of states and the circulating current density in a vortex corresponding to various levels of mean-field theories are predicted.