Phase Diagram for Ultracold Bosons in Optical Lattices and Superlattices

TL;DR

This paper analytically derives the finite-temperature phase diagram of the Bose-Hubbard model, describing superfluid, normal fluid, and Mott insulator phases in ultracold bosonic atoms within optical lattices and superlattices.

Contribution

It provides an exact mean-field solution for the phase boundaries and Mott lobes, advancing understanding of phase transitions in these quantum systems.

Findings

Exact expression for superfluid-normal fluid boundary

Analytic form of Mott lobes at zero temperature

Characterization of critical fractional fillings

Abstract

We present an analytic description of the finite-temperature phase diagram of the Bose-Hubbard model, successfully describing the physics of cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide the exact expression for the boundary between the superfluid and the normal fluid by solving the self-consistency equations involved in the mean-field approximation to the Bose-Hubbard model. The zero-temperature limit of such result supplies an analytic expression for the Mott lobes of superlattices, characterized by a critical fractional filling.