Variance of an anisotropic Bose-Einstein condensate

TL;DR

This paper investigates how trap anisotropy affects the density and variance of a Bose-Einstein condensate, revealing counterintuitive behaviors that can help characterize correlations in the system.

Contribution

It demonstrates the impact of trap anisotropy on BEC variance and density, highlighting the use of variance as a tool to analyze correlations in many-particle systems.

Findings

Variance can be smaller in wider density regions.

Position variance can be larger in narrower density directions.

Variance behavior reveals correlation strength in BECs.

Abstract

The anisotropy of a trap potential can impact the density and variance of a Bose-Einstein condensate (BEC) in an opposite manner. We exemplify this effect for both the ground state and out-of-equilibrium dynamics of structureless bosons interacting by a long-range inter-particle interaction and trapped in a two-dimensional single-well potential. We demonstrate that even when the density of the BEC is, say, wider along the $y$ direction and narrower along the $x$ direction, its position variance can actually be smaller and momentum variance larger in the $y$ direction than in the $x$ direction. This behavior of the variance in a many-particle system is counterintuitive. It suggests using the variance as a tool to characterize the strength of correlations along the $y$ and $x$ directions in a trapped BEC.