Networks of nonlinear optical cavities offer unprecedented opportunities for exploring novel phases of light and matter with potential applications to simulation and computation. In this talk, I will discuss the fundamental building-block of such networks: single nonlinear cavities.

First I will present measurements of the dynamic optical hysteresis of a semiconductor micro-cavity with a Kerr nonlinearity. Due to the influence of quantum fluctuations, the hysteresis area follows a double power law decay as a function of the scanning time across the bistability. I will explain how this behavior can be understood within the framework of the Kibble-Zurek mechanism, which describes the onset of non-adiabatic dynamics near a critical point. I will introduce the concept of a dissipative phase transition, and I will explain how to measure its main quantity – the Liouvillian gap – based on the statistics of quantum jumps in the nonlinear cavity.

In the second part of the talk, I will explain how the optical response of a micro-cavity is modified by a non-instantaneous nonlinearity. I will present dynamic optical hysteresis experiments based on tunable micro-cavities filled with thermal nonlinear media. The dynamic hysteresis area displays a non-monotonic behavior as the scanning time across the bistability approaches the thermal relaxation time. For large speeds, the non-instantaneous nonlinearity leads to a power law decay of the hysteresis area with a universal exponent.

I will conclude with perspectives for realizing lattices of bistable optical cavities, and for exploring non-Markovian nonlinear dynamics, in a tunable system at room-temperature.