Analysis of a trapped Bose-Einstein condensate in terms of position, momentum, and angular-momentum variance

TL;DR

This paper investigates the position, momentum, and angular-momentum variances of a 2D trapped Bose-Einstein condensate, comparing mean-field and many-body levels to understand correlations and depletion effects.

Contribution

It provides analytical and numerical analysis of variances in BECs, highlighting differences between mean-field and many-body descriptions and exploring their interconnections.

Findings

Variances differ significantly between mean-field and many-body models.

Depletion effects influence the angular-momentum variance.

Connections between different variances reveal underlying correlations.

Abstract

We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose-Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. The differences between the variances at the mean-field level, which are attributed to the shape of the BEC, and the variances at the many-body level, which incorporate depletion, are used to characterize position, momentum, and angular-momentum correlations in the BEC for finite systems and at the limit of an infinite number of particles where the bosons are $100\%$ condensed. Finally, we also explore inter-connections between the variances.