New Journal of Physics (Jan 2024)

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

  • H Alaeian,
  • M Soriente,
  • K Najafi,
  • S F Yelin

DOI
https://doi.org/10.1088/1367-2630/ad2414
Journal volume & issue
Vol. 26, no. 2
p. 023021

Abstract

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In 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 (MF) 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 MF 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.

Keywords