Power laws in the dynamic hysteresis of quantum nonlinear photonic resonators

In a wide class of systems, sweeping back and forth the driving amplitude of a nonlinear resonator produces a hysteresis cycle, which for electromagnetic resonators is referred to as optical bistability. For weak nonlinearities, it can be described by a semiclassical approach neglecting quantum fluctuations. It is known that quantum fluctuations induce switching between two classically stable branches. The steady-state is then unique and consists of a statistical mixture of the two branches. in other words, in the quantum regime (for large nonlinearities), there is no static hysteresis.
We show in this work that there is nonetheless a dynamic hysteresis in the quantum regime. By sweeping the driving amplitude in a finite time we show that the area of the hysteresis cycle exhibits a rich temporal power-law behavior, qualitatively different from semiclassical predictions. We connect this behavior to a nonadiabatic response of the system and establish a link with the Kibble-Zurek mechanism for quenched phase transitions.

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