Collective phases of strongly interacting cavity photons

TL;DR

This paper investigates the complex steady states and dynamical behaviors of strongly interacting driven photonic cavities, revealing phases with magnetic order, oscillations, and bistability, supported by both mean-field and quantum simulations.

Contribution

It introduces a mean-field phase diagram for driven-dissipative cavity arrays and connects these results with exact quantum simulations, highlighting collective switching dynamics.

Findings

Identification of canted antiferromagnetic and limit cycle phases.

Observation of collective bistability and switching behavior.

Short-range antiferromagnetic order in quantum simulations.

Abstract

We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-$\frac{1}{2}$ model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.