Stochastic resonance with a single metastable state: Thermal instability in NbN superconducting stripline resonators

Abstract

We study thermal instability in NbN superconducting stripline resonators. The system exhibits extreme nonlinearity near a bifurcation, which separates a monostable zone and an astable one. The lifetime of the metastable state, which is locally stable in the monostable zone, is measured near the bifurcation and the results are compared with a theory. Near bifurcation, where the lifetime becomes relatively short, the system exhibits strong amplification of a weak input modulation signal. We find that the frequency bandwidth of this amplification mechanism is limited by the rate of thermal relaxation. When the frequency of the input modulation signal becomes comparable or larger than this rate, the response of the system exhibits subharmonics of various orders.Stochastic resonance ͑SR͒ is a phenomenon in which metastability in nonlinear systems is exploited to achieve amplification of weak signals. 1-3 SR has been experimentally demonstrated in electrical, optical, superconducting, neuronal, and mechanical systems. 4-12 Usually, SR is achieved by operating the system in a region in which it has two metastable states and its response exhibits hysteresis. Under some appropriate conditions, a weak input signal, which modulates the transition rates between these states, can lead to synchronized noise-induced transitions, thus allowing strong amplification.In this Brief Report, we investigate SR and amplification in a superconducting ͑SC͒ NbN stripline resonator. Contrary to previous studies, we operate the system near a bifurcation between a monostable zone, in which the system has a single metastable state, and an astable zone, in which this state ceases to exist and the system lacks any steady states. In our previous studies, we have investigated several effects, e.g., strong amplification, 13 noise squeezing, 13 and response to optical illumination, 14,15 which occur near this bifurcation, and limit cycle oscillations, which are observed in the astable zone. 16,17 In the present work, we investigate experimentally and theoretically the response of the system to an amplitude modulated input signal and find an unusual SR mechanism that has both properties of extremely strong responsivity and nonhysteretic behavior. The frequency bandwidth of this mechanism is found to be limited by the rate of thermal relaxation. We find that rather unique subharmonics of various orders are generated when the modulation frequency becomes comparable or larger than the relaxation rate. Moreover, we measure the lifetime of the metastable state in the monostable zone near the bifurcation and compare the results with a theory.Our experiments are performed using a device that integrates a narrow microbridge into a SC stripline electromagnetic resonator. Design considerations, fabrication details, as well as resonance modes calculation can be found elsewhere. 14 The dynamics of our system can be captured by two coupled equations of motion, which are hereby briefly described ͑see Ref. 17 for a detailed derivation͒. Consider a resonator driven ...

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