Power-laws in the dynamic hysteresis of quantum nonlinear photonic resonators

TL;DR

This paper investigates the quantum dynamic hysteresis in driven-dissipative nonlinear photonic resonators, revealing power-law decay behaviors and the influence of system parameters, with implications for various physical platforms.

Contribution

It introduces a quantum analysis of dynamic hysteresis in nonlinear resonators, highlighting power-law behaviors and the role of non-adiabatic response regions, extending mean-field predictions.

Findings

Dynamic hysteresis exhibits a double power-law decay with sweep time.

Characteristic time depends on nonlinearity strength and detuning.

Hysteresis behavior persists in coupled resonator systems.

Abstract

We explore theoretically the physics of dynamic hysteresis for driven-dissipative nonlinear photonic resonators. In the regime where the semiclassical mean-field theory predicts bistability, the exact steady-state density matrix is known to be unique, being a statistical mixture of two states: in particular, no static hysteresis cycle of the excited population occurs as a function of the driving intensity. Here, we predict that in the quantum regime a dynamic hysteresis with a rich phenomenology does appear when sweeping the driving amplitude in a finite time. The hysteresis area as a function of the sweep time reveals a double power-law decay, with a behavior qualitatively different from the mean-field predictions. The dynamic hysteresis power-law in the slow sweep limit defines a characteristic time, which depends dramatically on the size of the nonlinearity and on the frequency detuning between the driving and the resonator. In the strong nonlinearity regime, the characteristic time oscillates as a function of the intrinsic system parameters due to multiphotonic resonances. We show that the dynamic hysteresis for the considered class of driven-dissipative systems is due to a non-adiabatic response region with connections to the Kibble-Zurek mechanism for quenched phase transitions. We also consider the case of two coupled driven-dissipative nonlinear resonators, showing that dynamic hysteresis and power-law behavior occur also in presence of correlations between resonators. Our theoretical predictions can be explored in a broad variety of physical systems, e.g., circuit QED superconducting resonators and semiconductor optical microcavities.