Bose--Hubbard Models Coupled to Cavity Light Fields

TL;DR

This paper explores the phase diagram and properties of Bose-Hubbard models coupled to cavity light fields, revealing polariton condensation, superradiant transitions, and the interplay of superfluidity and Mott phases.

Contribution

It introduces a comprehensive variational phase diagram for coupled cavity Bose-Hubbard systems, highlighting polariton condensation and novel phase transitions.

Findings

Identification of polariton formation within the Mott phase.

Discovery of a first-order transition between superradiant Mott and atomic superfluid phases.

Mean field predictions align well with exact diagonalization results.

Abstract

Recent experiments on strongly coupled cavity quantum electrodynamics present new directions in "matter-light" systems. Following on from our previous work [Phys. Rev. Lett. 102, 135301 (2009)] we investigate Bose-Hubbard models coupled to a cavity light field. We discuss the emergence of photoexcitations or "polaritons" within the Mott phase, and obtain the complete variational phase diagram. Exploiting connections to the super-radiance transition in the Dicke model we discuss the nature of polariton condensation within this novel state. Incorporating the effects of carrier superfluidity, we identify a first-order transition between the superradiant Mott phase and the single component atomic superfluid. The overall predictions of mean field theory are in excellent agreement with exact diagonalization and we provide details of superfluid fractions, density fluctuations, and finite size effects. We highlight connections to recent work on coupled cavity arrays.