# Quantum versus classical switching dynamics of driven-dissipative Kerr resonators

## TL;DR

This paper investigates the driven-dissipative dynamics of Kerr resonators in the mesoscopic regime, highlighting the importance of quantum effects and the limitations of classical models in describing switching behavior.

## Contribution

It provides a first-principles quantum analysis of switching dynamics in Kerr resonators, revealing the inadequacy of classical escape models and introducing a universal crossover parameter.

## Key findings

- Significant deviations from steady-state predictions in nonlinear resonance lineshapes.
- Emergence of a slow switching time scale longer than linear decay rates.
- Quantum treatment necessary for accurate switching rate predictions.

## Abstract

We report a first-principles study of the driven dissipative dynamics for Kerr oscillators in the mesoscopic regime. This regime is characterized by large Kerr nonlinearity, realized here using the nonlinear kinetic inductance of a large array of Josephson junctions. The experimentally measured nonlinear resonance lineshapes of the junction array modes show significant deviations from steady-state numerical predictions, and necessitate time-dependent numerical simulations indicative of strong measurement-induced dephasing in the system arising from the large cross-Kerr effect between array modes. Analytical and numerical calculations of switching rate corroborate this by showing the emergence of a slow time scale, which is much longer than the linear decay rate and is set by fluctuation-induced switching times in the bistable regime. Furthermore, our analysis shows that the usual quantum-activated escape treatment is inadequate for prediction of the switching rates at large frequency shifts caused by strong nonlinearities, necessitating a quantum treatment that utilizes the full system Liouvillian. Based on our analysis, we identify a universal crossover parameter that delineates the regimes of validity of semiclassical and quantum descriptions, respectively. Our work shows how dynamical switching effects in strongly nonlinear systems provide a platform to study quantum-to-classical transitions.