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

Published

October 12, 2021

Author(s)

E Calzetta, B- L. Hu, A M. Rey

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. Comparison of our analytic results with exact numerical solutions for $N$ particles in a one-dimensional lattice of $N=5, 7$ and 9 sites shows satisfactory agreement across the transition region.

Citation

Physical Review A (Atomic, Molecular and Optical Physics)

Pub Type

Journals

Keywords

Bogoliubov, Bose-Einstein condensate, density matrix, momentum distribution, Mott, optical lattices, pertubation theory, superfluid

Citation

Calzetta, E. , Hu, B. and Rey, A. (2021), Bose-Einstein Condensate Superfluid-Mott Insulator Transition in an Optical Lattice, Physical Review A (Atomic, Molecular and Optical Physics) (Accessed November 3, 2025)