Fluctuating Trajectories and Switching Rates of a Synthetic Two-Level System

The Kerr Parametric Oscillator (KPO) is a nonlinear resonator system that is often described as a synthetic two-level system. We reveal that activated switches between these levels follow a fluctuating and curving trajectory in phase space. Such fluctuations make it hard to establish a precise count, or even a useful definition, of the "lifetime" of the levels. Addressing this issue, we compare several methods to overcome this systemic noise, and estimate a lifetime for the levels. Moreover, we establish that a peak in the Allan variance of fluctuations can also be used to determine the levels' lifetime. Our work provides a basis for characterizing KPO networks for simulated annealing.