Classical critical dynamics in quadratically driven Kerr resonators

Abstract

Driven-dissipative kerr lattices with two-photon driving are experimentally relevant systems known to exhibit a symmetry-breaking phase transition, which belongs to the universality class of the thermal Ising model for the parameter regime studied here. In this work, we perform finite-size scaling of this system as it is quenched to the transition and the dynamical critical exponent is found to be compatible with $z\approx 2.18$ corresponding with metropolis dynamics in classical simulations. Furthermore, we show that the Liouvillian gap scales with the same exponent, similar to scaling of the Hamiltonian gap at quantum phase transitions in closed systems.

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Cited by in corpus (9)

• Driven-dissipative phase transition in a Kerr oscillator: From semiclassical $\mathcal{P}\mathcal{T}$ symmetry to quantum fluctuations
• Kibble-Zurek mechanism in driven-dissipative systems crossing a non-equilibrium phase transition
• Dynamical hysteresis properties of the driven-dissipative Bose-Hubbard model with a Gutzwiller Monte Carlo approach
• Vortices in nonequilibrium photon condensates
• Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems
• Emergent Kardar-Parisi-Zhang phase in quadratically driven condensates
• Analogue Spin Simulators: How to keep the Amplitude Homogeneous
• Excited-State Adiabatic Quantum Computation Started with Vacuum States
• Optical resonators constitute a universal spin simulator