A Quantum Theory of Cold Bosonic Atoms in Optical Lattices

TL;DR

This paper develops an approximate quantum theory for cold bosonic atoms in optical lattices, capturing the superfluid to Mott insulator transition and applicable to various lattice configurations.

Contribution

It introduces a novel variable transformation approach that qualitatively describes both superfluid and insulator phases in optical lattices.

Findings

Successfully models the superfluid to Mott insulator transition.

Applicable to uniform, frustrated, and inhomogeneous lattice systems.

Provides a simple yet effective theoretical framework.

Abstract

Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a Mott insulator as the lattice potential depth is increased. We describe an approximate theory of interacting bosons in optical lattices which provides a qualitative description of both superfluid and insulator states. The theory is based on a change of variables in which the boson coherent state amplitude is replaced by an effective potential which promotes phase coherence between different number states on each lattice site. It is illustrated here by applying it to uniform and fully frustrated lattice cases, but is simple enough that it can easily be applied to spatially inhomogeneous lattice systems.