Interacting bosons in an optical lattice

TL;DR

This paper investigates the phases and excitations of strongly interacting Bose gases in optical lattices using a functional-integral approach, covering mean-field and fluctuation effects across different regimes.

Contribution

It extends the mean-field description of Bose gases in optical lattices by incorporating Gaussian fluctuations and renormalized parameters for dense regimes.

Findings

Phase diagrams for Bose-Einstein condensate and Mott insulator states

Spectrum of quasiparticle excitations analyzed

Static structure factor computed

Abstract

Several models of a strongly interacting Bose gas in an optical lattice are studied within the functional-integral approach. The one-dimensional Bose gas is briefly discussed. Then the Bose-Einstein condensate and the Mott insulator of a three-dimensional Bose gas are described in mean-field approximation, and the corresponding phase diagrams are evaluated. Other characteristic quantities, like the spectrum of quasiparticle excitations and the static structure factor, are obtained from Gaussian fluctuations around the mean-field solutions. We discuss the role of quantum and thermal fluctuations, and determine the behavior of physical quantities in terms of density and temperature of the Bose gas. In particular, we study the dilute limit, where the mean-field equation becomes the Gross-Pitaevskii equation. This allows us to extend the Gross-Pitaevskii equation to the dense regime by introducing renormalized parameters in the latter.