Emergent equilibrium in many-body optical bistability

TL;DR

This paper reveals that the steady state of the driven-dissipative Bose-Hubbard model exhibits an emergent equilibrium behavior akin to a classical Ising model, bridging non-equilibrium quantum optics and classical statistical mechanics.

Contribution

It demonstrates that a non-equilibrium lattice model of optical bistability can be effectively described by an emergent equilibrium Ising model in a certain limit, linking driven-dissipative quantum systems to classical phase transitions.

Findings

The steady state maps onto a classical Ising model.

Numerical Langevin simulations support the emergent equilibrium picture.

The phase transition aligns with model A of Hohenberg-Halperin classification.

Abstract

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.