Finite temperature theory of superfluid bosons in optical lattices

TL;DR

This paper develops a finite temperature theoretical framework for superfluid bosons in optical lattices, extending the Bose-Hubbard model to shallow lattices and excited bands, and demonstrates improved agreement with experiments.

Contribution

It introduces an extended Bose-Hubbard model applicable to shallow lattices and excited bands, combined with a mean-field approach for accurate finite temperature predictions.

Findings

Enhanced agreement with experimental data

Effective numerical implementation for 3D systems

Highlights importance of extended model features

Abstract

A practical finite temperature theory is developed for the superfluid regime of a weakly interacting Bose gas in an optical lattice with additional harmonic confinement. We derive an extended Bose-Hubbard model that is valid for shallow lattices and when excited bands are occupied. Using the Hartree-Fock-Bogoliubov-Popov mean-field approach, and applying local density and coarse-grained envelope approximations, we arrive at a theory that can be numerically implemented accurately and efficiently. We present results for a three-dimensional system, characterizing the importance of the features of the extended Bose-Hubbard model and compare against other theoretical results and show an improved agreement with experimental data.