Nonequilibrium Kramers Turnover in a Kerr Parametric Oscillator

Abstract: Activation processes govern noise-induced switching between long-lived states. In an equilibrium double well, the thermally activated switching rate exhibits a prefactor with a nonmonotonic dependence on environmental coupling, a foundational crossover known as Kramers turnover. Here, we demonstrate a Kramers turnover analogue in a Kerr parametric oscillator, a driven-dissipative nonlinear system featuring two stable phase states. First, we analytically establish turnover physics in this out-of-equilibrium setting. There, the strong physical correlation between the activation barrier and intrinsic damping fundamentally obscures the underlying turnover physics. To overcome this limitation, we rescale the rotating-frame dynamics and introduce a tunable effective friction controlled entirely by the parametric drive. This rescaling comes at the cost of a concurrent rescaling of the effective temperature. Exploiting this simultaneous scaling, we leverage the effective temperature to extract the turnover directly from temperature-dependent observations. Subsequently, measuring noise-induced phase slips in a micro-electromechanical device, we observe a distinct crossover in the prefactor's temperature dependence. Our results unambiguously isolate the out-of-equilibrium turnover regime and highlight that the competition between dissipation and fluctuations profoundly shapes activation dynamics also beyond equilibrium.