# Out-of-equilibrium physics in driven dissipative coupled resonator arrays

## TL;DR

This paper reviews the out-of-equilibrium physics of driven dissipative coupled resonator arrays, highlighting phenomena like photon fermionisation, crystallisation, and quantum Hall effects, and discusses theoretical models and numerical methods used to study them.

## Contribution

It provides a comprehensive overview of the physics in driven dissipative resonator arrays, emphasizing non-equilibrium phenomena and the theoretical frameworks used.

## Key findings

- Photon fermionisation observed in driven systems
- Crystallisation phenomena in resonator arrays
- Photonic quantum Hall effects out of equilibrium

## Abstract

Coupled resonator arrays have been shown to exhibit interesting many- body physics including Mott and Fractional Hall states of photons. One of the main differences between these photonic quantum simulators and their cold atoms coun- terparts is in the dissipative nature of their photonic excitations. The natural equi- librium state is where there are no photons left in the cavity. Pumping the system with external drives is therefore necessary to compensate for the losses and realise non-trivial states. The external driving here can easily be tuned to be incoherent, coherent or fully quantum, opening the road for exploration of many body regimes beyond the reach of other approaches. In this chapter, we review some of the physics arising in driven dissipative coupled resonator arrays including photon fermionisa- tion, crystallisation, as well as photonic quantum Hall physics out of equilibrium. We start by briefly describing possible experimental candidates to realise coupled resonator arrays along with the two theoretical models that capture their physics, the Jaynes-Cummings-Hubbard and Bose-Hubbard Hamiltonians. A brief review of the analytical and sophisticated numerical methods required to tackle these systems is included.