Cratered Lorentzian response of driven microwave superconducting nanowire-bridged resonators: Oscillatory and magnetic-field induced stochastic states

We report on observations of a superconductor-normal pulsing regime in microwave (GHz) coplanar waveguide resonators consisting of superconducting MoGe films interrupted by a gap that is bridged by one or more suspended superconducting nanowires. This regime, which involves MHz-frequency oscillations in the amplitude of the supercurrent in the resonator, is achieved when the steady-state amplitude of the current in the driven resonator exceeds the critical current of the nanowires. Thus we are able to determine the temperature dependence of the critical current, which agrees well with the corresponding Bardeen formula. The pulsing regime manifests itself as an apparent crater on top of the fundamental Lorentzian peak of the resonator. Once the pulsing regime is achieved at a fixed drive power, however, it remains stable for a range of drive frequencies corresponding to subcritical steady-state currents in the resonator. We develop a phenomenological model of resonator-nanowire systems from which we are able to obtain a quantitative description of the amplitude oscillations and also, inter alia, to investigate thermal relaxation processes in superconducting nanowires. For the case of resonators comprising two parallel nanowires and subject to an external magnetic field, we find field-driven oscillations of the onset power for the amplitude oscillations, as well as the occurrence (for values of the magnetic field that strongly frustrate the nanowires) of a distinct steady state in which the pulsing is replaced by stochastic amplitude fluctuations. We conclude by giving a brief discussion of how circuit-quantum electrodynamics-based systems have the potential to facilitate nondestructive measurements of the current-phase relationship of superconducting nanowires and, hence, of the rate at which quantum phase slips take place in superconducting nanowires.