Escape rate of metastable states in a driven NbN superconducting microwave resonator

We study thermal instability and formation of local hot spots in a driven nonlinear NbN superconducting microwave resonator. White noise injected into the resonator results in transitions between the metastable states via a process consisting of two stages. In the first stage, the input noise entering the system induces fluctuations in the resonator mode. While in the second one, these mode fluctuations result in phase transitions of the hot spot due to induced temperature fluctuations. The associated noise-activated escape rate is calculated theoretically and measured also experimentally by means of driving the system into stochastic resonance. A comparison between theory and experiment yields a partial agreement.