Condensate deformation and quantum depletion of Bose-Einstein condensates in external potentials

TL;DR

This paper uses inhomogeneous Bogoliubov theory to analyze how external potentials deform Bose-Einstein condensates and cause quantum depletion, providing analytical results for various potential types.

Contribution

It introduces an analytical approach to quantify condensate deformation and quantum depletion in external potentials, extending understanding of inhomogeneous Bose-Einstein condensates.

Findings

Potential depletion is a small correction to homogeneous depletion.

Analytical results are derived for weak lattices and correlated random potentials.

Universal results are obtained in the Thomas-Fermi limit.

Abstract

The one-body density matrix of weakly interacting, condensed bosons in external potentials is calculated using inhomogeneous Bogoliubov theory. We determine the condensate deformation caused by weak external potentials on the mean-field level. The momentum distribution of quantum fluctuations around the deformed ground state is obtained analytically, and finally the resulting quantum depletion is calculated. The depletion due to the external potential, or potential depletion for short, is a small correction to the homogeneous depletion, validating our inhomogeneous Bogoliubov theory. Analytical results are derived for weak lattices and spatially correlated random potentials, with simple, universal results in the Thomas-Fermi limit of very smooth potentials.