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arXiv:cond-mat/0504582 · Physical Review B

Nonlinear dynamics in the resonance line shape of NbN superconducting resonators

Baleegh Abdo, Eran Segev, Oleg Shtempluck, Eyal Buks

Published Apr 17, 2006• 44 citations
arXivHTMLPDF

Abstract

We report on unusual nonlinear dynamics observed in the resonance response of $\mathrm{NbN}$ superconducting microwave resonators. The nonlinear dynamics which occurs at relatively low input powers (2--4 orders of magnitude lower than Nb) includes among others, jumps in the resonance line shape, hysteresis loops changing direction, and resonance frequency shift. These effects are measured herein using varying input power, applied magnetic field, white noise, and rapid frequency sweeps. Based on these measurement results, we consider a hypothesis according to which local heating of weak links forming at the boundaries of the $\mathrm{NbN}$ grains is responsible for the observed behavior, and we show that most of the experimental results are qualitatively consistent with such a hypothesis.

DOI
10.1103/physrevb.73.134513

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In this paper, we report some extraordinary nonlinear dynamics measured in the resonance curve of NbN superconducting stripline microwave resonators. Among the nonlinearities observed: abrupt bifurcations in the resonance response at relatively low input powers, asymmetric resonances, multiple jumps within the resonance band, resonance frequency drift, frequency hysteresis, hysteresis loops changing direction and critical coupling phenomenon. Weak links in the NbN grain structure are hypothesized as the source of the nonlinearities
Some results of an investigation of nonlinear behavior of NbN and YBa2Cu3O7-x films at microwaves are presented. Nonlinear microwave properties of superconducting films are analyzed on the basis of dynamic Current Voltage Characteristics (CVC) measured from the film response to the short duration video pulse. Conversion loss of the microwave signal into the intermediate frequency signal under various local oscillator power has been obtained from this analysis. The experimental data for the mixing of two microwave signals are described. Mixing effect was observed on superconducting NbN and YBa2Cu3O7-x film elements in microbridge and coplanar line forms. Conversion loss of about 20 dB was obtained in the running-wave regime.
This experiment is designed to compare the feedback from an altered superconductor resonator with a conventional, unaltered superconductor resonator. Superconducting transmission lines are patterned on a lanthanum aluminium substrate chip with a geometry that resonates within the microwave range. Nonlinearities, distortion of the signals in the superconductor, can be engineered into the transmission line using an ion beam or other artificial source of radiation. The sample in this experiment, thin-film yttrium barium copper oxide: YBCO was sent to a facility in Italy to be engineered with a nonlinearity and then characterized in a low temperature (77 K) cryostat. This means that the power dependence of a traditional resonator will differ greatly from this sample. Two key figures of merit of superconducting resonators are their critical power, where the power input to the resonator is most absorbed, and critical frequency of the sample, the frequency at which the critical power occurs. Both were found to vary with temperature, and at high incident power the frequency response of the resonator begins to experience deformation. The change of the power response as frequency is swept through (bending) and the hysteresis in the curve (bifurcation) form the core disparities between traditional superconducting resonators and those with engineered nonlinearities.
We discuss how reactive and dissipative nonlinearities affect the intrinsic response of superconducting thin-film resonators. We explain how most, if not all, of the complex phenomena commonly seen can be described by a model in which the underlying resonance is a single-pole Lorentzian, but whose centre frequency and quality factor change as external parameters, such as readout power and frequency, are varied. What is seen during a vector-network-analyser measurement is series of samples taken from an ideal Lorentzian that is shifting and spreading as the readout frequency is changed. According to this model, it is perfectly proper to refer to, and measure, the resonant frequency and quality factor of the underlying resonance, even though the swept-frequency curves appear highly distorted and hysteretic. In those cases where the resonance curve is highly distorted, the specific shape of the trajectory in the Argand plane gives valuable insights into the second-order physical processes present. We discuss the formulation and consequences of this approach in the case of nonlinear kinetic inductance, two-level-system loss, quasiparticle generation, and a generic model based on a power-law form. The generic model captures the key features of specific dissipative nonlinearities, but additionally leads to insights into how general dissipative processes create characteristic forms in the Argand plane. We provide detailed formulations in each case, and indicate how they lead to the wide variety of phenomena commonly seen in experimental data. We also explain how the properties of the underlying resonance can be extracted from this data. Overall, our paper provides a self-contained compendium of behaviour that will help practitioners interpret and determine important parameters from distorted swept-frequency measurements.
Abstract We discuss how reactive and dissipative nonlinearities affect the intrinsic response of superconducting thin-film resonators. We explain how most, if not all, of the complex phenomena commonly seen can be described by a model in which the underlying resonance is a single-pole Lorentzian, but whose centre frequency and quality factor change as external parameters, such as readout power and frequency, are varied. What is seen during a vector-network-analyser measurement is series of samples taken from an ideal Lorentzian that is shifting and spreading as the readout frequency is changed. According to this model, it is perfectly proper to refer to, and measure, the resonant frequency and quality factor of the underlying resonance, even though the swept-frequency curves appear highly distorted and hysteretic. In those cases where the resonance curve is highly distorted, the specific shape of the trajectory in the Argand plane gives valuable insights into the second-order physical processes present. We discuss the formulation and consequences of this approach in the case of nonlinear kinetic inductance, two-level-system loss, quasiparticle generation, and a generic model based on a power-law form. The generic model captures the key features of specific dissipative nonlinearities, but additionally leads to insights into how general dissipative processes create characteristic forms in the Argand plane. We provide detailed formulations in each case, and indicate how they lead to the wide variety of phenomena commonly seen in experimental data. We also explain how the properties of the underlying resonance can be extracted from this data. Overall, our paper provides a self-contained compendium of behaviour that will help practitioners interpret and determine important parameters from distorted swept-frequency measurements.