Bose-Einstein Quantum Phase Transition in an Optical Lattice Model

TL;DR

This paper rigorously analyzes a lattice model showing a quantum phase transition between Bose-Einstein condensation and Mott insulator phases driven by the optical lattice strength and temperature, highlighting the role of interactions.

Contribution

The paper introduces a rigorous analysis of a lattice gas model demonstrating a quantum phase transition between BEC and Mott insulator phases influenced by an external periodic potential.

Findings

BEC occurs at small potential strength and temperature

Mott insulator phase appears at large potential strength or temperature

Condensation always occurs into the zero momentum mode

Abstract

Bose-Einstein condensation (BEC) in cold gases can be turned on and off by an external potential, such as that presented by an optical lattice. We present a model of this phenomenon which we are able to analyze rigorously. The system is a hard core lattice gas at half-filling and the optical lattice is modeled by a periodic potential of strength $\lambda$. For small $\lambda$ and temperature, BEC is proved to occur, while at large $\lambda$ or temperature there is no BEC. At large $\lambda$ the low-temperature states are in a Mott insulator phase with a characteristic gap that is absent in the BEC phase. The interparticle interaction is essential for this transition, which occurs even in the ground state. Surprisingly, the condensation is always into the $p=0$ mode in this model, although the density itself has the periodicity of the imposed potential.