Physics of Superconducting Travelling-Wave Parametric Amplifiers

Abstract

Superconducting travelling-wave parametric amplifiers (TWPAs) are ultra-low-noise amplifiers that achieve amplification through the nonlinear kinetic inductance of superconductors. These devices can have near quantum-limited noise performance, and have important applications in quantum information systems, ground-based and space-based astronomical observatories, and fundamental quantum science experiments. In the first half of this thesis, I describe work on developing a comprehensive set of theoretical and numerical models of TWPAs. Although TWPAs are the primary subject of this thesis, the techniques and models described are relevant to other research areas such as superconducting resonators, nonlinear superconductivity, and parametric wave-mixing. At material-level, I study the physics of thin-film superconductors by using Usadel's equations, which are derived from the microscopic BCS theory. I investigate the supercurrent nonlinearity that is intrinsic to the physics of superconductors, and calculate its effect on the electrodynamics of superconducting materials. At component-level, I develop electromagnetic models for superconducting transmission lines using field analysis and conformal mapping technique. The models are suitable for microstrip transmission lines and coplanar waveguide architectures. At device-level, I analyse the effect of nonlinear wave-mixing on a transmission line by using a travelling-wave coupled-mode method. The method produces key amplifier performance metrics such as gain, bandwidth and saturation power. Finally, I develop a quantum description of nonlinear wave-mixing on a transmission line by spatially evolving quantised modes using momentum operators. This quantum analysis gives quantitative predictions of the effect of thermal noise, and confirms that the noise limit of an ideal TWPA is indeed the standard quantum limit. In the second half of this thesis, I describe the design and measurement of TWPAs based on microstrip transmission line and coplanar waveguide architectures. Using the analysis framework described in the first half of this thesis, I designed TWPAs to achieve high kinetic inductance fractions, high gains, and close to 50 Ohm characteristic impedance. I characterised these TWPAs and measured their gain performance. I also operated superconducting resonators as resonator amplifiers. I report measurements of > 20 dB gain for both TWPAs and resonator amplifiers. My results suggest that, in many material systems, the underlying inductive/resistive nonlinearities have finite response-times, which often limit the gain-bandwidth product. By including the finite response-time of the inductive nonlinearity in my TWPA model, I obtained excellent agreement between the proposed theory and experimental results.