Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

• Main Author: Ofir E. Alon
• Format: Article
• Language: English
• Published: MDPI AG 2019-11-01
• Series: Symmetry
• Subjects: bose–einstein condensates; density; position variance; momentum variance; angular-momentum variance; harmonic-interaction model; mctdhb
• Online Access: https://www.mdpi.com/2073-8994/11/11/1344

We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose&#8722;Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. Explicitly, we study the ground state of the anisotropic harmonic-interaction model in two spatial dimensions analytically and the out-of-equilibrium dynamics of repulsive bosons in tilted two-dimensional annuli numerically accurately by using the multiconfigurational time-dependent Hartree for bosons method. 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mn>100</mn> <mo>%</mo> </mrow> </semantics> </math> </inline-formula> condensed. Finally, we also explore inter-connections between the variances.