Noise-resilient phase transitions and limit-cycles in coupled Kerr oscillators

Abstract

n recent years, there has been considerable focus on exploring driven-dissipative quantum systems, as they exhibit distinctive dissipation-stabilized phases. Among them, dissipative time crystal is
a unique phase emerging as a shift from disorder or stationary states to periodic behaviors. However,
understanding the resilience of these non-equilibrium phases against quantum fluctuations remains
unclear. This study addresses this query within a canonical parametric quantum optical system,
specifically, a multi-mode cavity with self- and cross-Kerr non-linearity. Using mean-field theory we
obtain the phase diagram and delimit the parameter ranges that stabilize a non-stationary limit-cycle phase. Leveraging the Keldysh formalism, we study the unique spectral features of each phase.
Further, we extend our analyses beyond the mean-field theory by explicitly accounting for higher-
order correlations through cumulant expansions. Our findings unveil insights into the modifications
of the open quantum systems phases, underscoring the significance of quantum correlations in non-
equilibrium steady states. Importantly, our results conclusively demonstrate the resilience of the
non-stationary phase against quantum fluctuations, rendering it a dissipation-induced genuine
quantum synchronous phase.