Applications of density matrices in a trapped Bose gas

TL;DR

This paper explores how interparticle correlations affect the properties of a trapped Bose gas at zero temperature, using analytical and numerical methods to analyze quantum information measures and density distributions.

Contribution

It provides analytical expressions and numerical calculations for correlation effects on one- and two-body properties, including quantum information measures, in a trapped Bose gas.

Findings

Correlations significantly influence quantum information measures.

Analytical and numerical methods agree on the effects of correlations.

Density distributions are affected by the strength of short-range interactions.

Abstract

An overview of the Bose-Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the lowest order cluster expansion. Analytical expressions for the one- and two-body properties of the Bose gas are derived using Jastrow-type correlation function. In addition numerical calculations of the natural orbitals and natural occupation numbers are also carried out. Special effort is devoted for the calculation of various quantum information properties including Shannon entropy, Onicescu informational energy, Kullback-Leibler relative entropy and the recently proposed Jensen-Shannon divergence entropy. The above quantities are calculated for the trapped Bose gases by comparing the correlated and uncorrelated cases as a function of the strength of the short-range correlations. The Gross-Piatevskii equation is solved giving the density distributions in position and momentum space, which are employed to calculate quantum information properties of the Bose gas.