Bose - Einstein Condensate Superfluid-Mott Insulator Transition in an Optical Lattice

TL;DR

This paper develops an analytical model for the Bose-Einstein condensate superfluid-Mott insulator transition in an optical lattice, providing a unified expression for the momentum distribution across both regimes.

Contribution

It introduces an analytic formula that interpolates between superfluid and Mott insulator regimes, enhancing understanding of the transition in cold bosonic gases.

Findings

Derived an explicit expression for the momentum distribution.

Unified description bridging superfluid and Mott regimes.

Applicable to experimental measurements of condensate properties.

Abstract

We present in this paper an analytical model for a cold bosonic gas on an optical lattice (with densities of the order of 1 particle per site) targeting the critical regime of the Bose - Einstein Condensate superfluid - Mott insulator transition. We focus on the computation of the one - body density matrix and its Fourier transform, the momentum distribution which is directly obtainable from `time of flight'' measurements. The expected number of particles with zero momentum may be identified with the condensate population, if it is close to the total number of particles. Our main result is an analytic expression for this observable, interpolating between the known results valid for the two regimes separately: the standard Bogoliubov approximation valid in the superfluid regime and the strong coupling perturbation theory valid in the Mott regime.