Quantum Phase Transitions of Light in the Dicke-Bose-Hubbard model

TL;DR

This paper explores quantum phase transitions of light in the Dicke-Bose-Hubbard model with multiple two-level atoms, deriving eigenenergies and phase diagrams to understand transitions from Mott insulator to superfluid states.

Contribution

It extends the Dicke-Bose-Hubbard model to arbitrary atom numbers, providing a complete phase diagram and analyzing the effects of increasing atom count on Mott lobes.

Findings

Complete phase diagram for two atoms on resonance.

Mott lobes diminish as atom number increases.

Method applicable to arbitrary atom numbers.

Abstract

We extend the idea of quantum phase transitions of light in atom-photon system with Dicke-Bose-Hubbard model for arbitrary number of two-level atoms. The formulations of eigenenergies, effective Rabi frequencies, and critical chemical potentials for two atoms are derived. With a self-consistent method, we obtain a complete phase diagram for two two-level atoms on resonance, which indicates the transition from Mott insulator to superfluidity and with a mean excitations diagram for confirmation. We illustrate the generality of the method by constructing the dressed-state basis for arbitrary number of two-level atoms. In addition, we show that the Mott insulator lobes in the phase diagrams will smash out with the increase of atom numbers. The results of this work provide a step for studying the effects with combinations of Dicke-like and Hubbard-like models to simulate strongly correlated electron systems using photons.