Nonlinear Effects in Superconducting Thin Film Microwave Resonators

  1. Christopher N Thomas,
  2. Stafford Withington,
  3. Zhenyuan Sun,
  4. Tess Skyrme,
  5. and David J. Goldie
We discuss how reactive and dissipative non-linearities 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 non-linear 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 non-linearities, 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.

Loss and Saturation in Superconducting Travelling-Wave Parametric Amplifiers

  1. Songyuan Zhao,
  2. Stafford Withington,
  3. David J. Goldie,
  4. and Chris N. Thomas
We have developed a coupled-mode analysis framework for superconducting travelling-wave parametric amplifiers using the full Telegrapher’s equations to incorporate loss-related
behaviour. Our model provides an explanation of previous experimental observations regarding loss in amplifiers, advantages of concatenating amplifiers to achieve high gains, and signal gain saturation. This work can be used to guide the design of amplifiers in terms of the choice of material systems, transmission line geometry, operating conditions, and pump strength.

Electromagnetic models for multilayer superconducting transmission lines

  1. Songyuan Zhao,
  2. Stafford Withington,
  3. David J. Goldie,
  4. and Chris N. Thomas
Thin-film superconducting transmission lines play important roles in many signal transmission and detection systems, including qubit coupling and read-out schemes, electron spin resonance
systems, parametric amplifiers, and various ultra high sensitivity detectors. Here we present a rigorous method for computing the electromagnetic behaviour of superconducting microstrip transmission lines and coplanar waveguides. Our method is based on conformal mapping, and is suitable for both homogeneous superconductors and proximity-coupled multilayers. We also present an effective conductivity approximation of multilayers, thereby allowing the multilayers to be analysed using existing electromagnetic design software. We compute the numerical results for Al-Ti bilayers and discuss the validity of our full computation and homogeneous approximation.