Condensate fraction of cold gases in non-uniform external potential

TL;DR

This paper introduces an iterative computational method to accurately determine the condensate fraction and eigenfunction in inhomogeneous Bose gases without continuous symmetries, validated through Monte Carlo simulations.

Contribution

The authors develop and validate a new iterative procedure for calculating condensate properties in complex Bose systems lacking symmetry.

Findings

Validated the iterative method with diffusion Monte Carlo simulations.

Established relationships between superfluid, condensed, and zero-momentum fractions.

Demonstrated applicability to inhomogeneous Bose gases in optical lattices.

Abstract

Exact calculation of the condensate fraction in multi-dimensional inhomogeneous interacting Bose systems which do not possess continuous symmetries is a difficult computational problem. We have developed an iterative procedure which allows to calculate the condensate fraction as well as the corresponding eigenfunction of the one-body density matrix. We successfully validate this procedure in diffusion Monte Carlo simulations of a Bose gas in an optical lattice at zero temperature. We also discuss relation between different criteria used for testing coherence in cold Bose systems, such as fraction of particles that are superfluid, condensed or are in the zero-momentum state.