Characterizing noise-induced lifetime of a phase state in a Kerr nonlinear resonator

We compare the suitability of several mathematical methods to characterize the lifetime of two-level systems. The methods deal in different ways with random-walk fluctuations during a switch. Such fluctuations are not captured by a simple telegraph-noise picture and can lead to a significant overestimation of the switching rate. We show that this problem can be avoided by choosing the correct counting method. In addition to known methods relying on thresholds and the power spectral density of fluctuations, we establish that a peak in the Allan variance of fluctuations can be used to determine the lifetime. As a simple, classical test system, we utilize a nonlinear Kerr resonator driven into parametric oscillations regime, whose stable solutions mimic the physics of a single spin. We also provide an outlook of how our methods can be used to study Kramer's turnover in the synthetic quasi-potential of a parametric oscillator.