Novel self-sustained modulation in superconducting stripline resonators

We study thermal instability in a driven superconducting NbN stripline resonator integrated with a microbridge. A monochromatic input drive is injected into the resonator and the response is measured as a function of the frequency and amplitude of the drive. Inside a certain zone of the frequency-amplitude plane the system has no steady state, and consequently selfsustained modulation of the reflected power off the resonator is generated. A theoretical model, according to which the instability originates by a hotspot forming in the microbridge, exhibits a good quantitative agreement with the experimental results. Copyright c © EPLA, 2007 Nonlinear effects in superconductors are important for both basic science and technology. A strong nonlinearity may be exploited to demonstrate some important quantum phenomena in the microwave domain, such as quantum squeezing [1–3] and experimental observation of the so-called dynamical Casimir effect [4]; whereas technologically, these effects may allow some intriguing applications such as bifurcation amplifiers for quantum measurements [5,6] and resonant readout of qubits [7]. In this work we study the response of a superconducting (SC) microwave stripline resonator to a monochromatic injected signal. We find that there is a certain range of driving parameters, in which a novel nonlinear phenomenon emerges, and self-sustained modulation (SM) of the reflected power off the resonator is generated by the resonator. That is, the resonator undergoes limit-cycle oscillations ranging between several to tens of megahertz. A theoretical model which attributes the SM to a thermal instability yields a good agreement with the experimental results. A similar phenomenon was briefly reported in the ’60s [8–11] in dielectric resonators which were partially coated by a SC film, but it was not thoroughly investigated and therefore its significance was somewhat overlooked. This phenomenon is of a significant importance as it introduces an extreme nonlinear mechanism, which is by far stronger than any other nonlinearity observed before in SC resonators [12]. It results in high intermodulation gain, substantial noise squeezing, period doubling of (a)E-mail: [email protected] various orders [12], and strong coupling between resonance modes. Our device (figs. 1(b)-(d)) integrates a narrow microbridge into a SC stripline ring resonator. The impedance of the microbridge strongly affects the resonance modes of the resonator and thus its resonance frequencies can be tuned by either internal (Joule self-heating) or external (infrared illumination [13]) perturbations [14]. Further design considerations, fabrication details as well as resonance modes calculation can be found elsewhere [13]. The experiments are performed using the setup depicted in fig. 1(a). The resonator is driven by a monochromatic tone at an angular frequency ωp, and the reflected power is measured by a spectrum analyzer in the frequency domain and an oscilloscope in the time domain. Measurements are carried out while the device is fully immersed in liquid helium. Figure 2 shows typical experimental and numerical results of the SM phenomenon in the frequency domain. The resonator is driven at the resonance frequency of the third mode f3, and the dependence of the SM on the pump power at the input of the resonator is investigated. At relatively low and relatively high input power ranges (Ppump −33.25 dBm ∪ Ppump −23.7 dBm) the response of the resonator is linear, namely, the reflected power contains a single spectral component at the frequency of the driving pump tone ωp. In between these power ranges, regular SM of the reflected power occurs (see panel (b), subplots (ii), (iv)). It is manifested by rather strong and sharp sidebands, which extend over several hundred megahertz at