Bose-Hubbard Model: Relation Between Driven-Dissipative Steady-States and Equilibrium Quantum Phases

TL;DR

This paper analytically explores the steady-states of the driven-dissipative Bose-Hubbard model, revealing mixed photon states, phase transitions, and limitations of semiclassical approaches in describing strongly correlated regimes.

Contribution

It provides analytical solutions for the mean-field master equation, identifying novel mixed states and clarifying the phase diagram of the driven-dissipative Bose-Hubbard model.

Findings

Discovery of statistical mixtures with Fock state coherence

Identification of a critical tunneling strength for phase crossover

Explanation of antibunching and superbunching phenomena

Abstract

We present analytical solutions for the mean-field master equation of the driven-dissipative Bose-Hubbard model for cavity photons, in the limit of both weak pumping and weak dissipation. Instead of pure Mott insulator states, we find statistical mixtures with the same second-order coherence as a Fock state with n photons, but a mean photon number of n/2. These mixed states occur when n pump photons have the same energy as n interacting photons inside the nonlinear cavity and survive up to a critical tunneling coupling strength, above which a crossover to classical coherent state takes place. We also explain the origin of both antibunching and superbunching predicted by P-representation mean-field theory at higher pumping and dissipation. In particular, we show that the strongly correlated region of the associated phase diagram cannot be described within the semiclassical Gross-Pitaevski approach.