Beyond Gross-Pitaevskii:local density vs. correlated basis approach for trapped bosons

TL;DR

This paper compares the local density approximation and a correlated basis approach to study the ground state of trapped Bose hard-spheres, assessing the accuracy of the Gross-Pitaevskii equation with respect to interatomic correlations.

Contribution

It introduces a correlated wave function approach and evaluates higher order corrections beyond Gross-Pitaevskii for trapped bosons.

Findings

Correlation effects are significant at particle numbers similar to experimental conditions.

Higher order low density expansion terms impact the energy by a few percent.

Explicit correlations improve the accuracy of ground state descriptions.

Abstract

We study the ground state of a system of Bose hard-spheres trapped in an isotropic harmonic potential to investigate the effect of the interatomic correlations and the accuracy of the Gross-Pitaevskii equation. We compare a local density approximation, based on the energy functional derived from the low density expansion of the energy of the uniform hard sphere gas, and a correlated wave function approach which explicitly introduces the correlations induced by the potential. Both higher order terms in the low density expansion, beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of the order of percent when the number of trapped particles becomes similar to that attained in recent experiments.