Superconducting Ring Resonators: Modelling, Simulation, and Experimental Characterisation

TL;DR

This paper provides a comprehensive theoretical and experimental analysis of superconducting ring resonators, highlighting their microwave behavior, mode coupling, and potential applications in quantum technologies.

Contribution

It introduces new models for superconducting ring resonators, validates them experimentally, and explores mode phenomena like frequency splitting and rotation in high-Q devices.

Findings

Close agreement between theory and microwave measurements

Frequency splitting and mode rotation are prevalent in coupled degenerate modes

High-Q resonators distinctly resolve mode phenomena

Abstract

We present a theoretical and experimental study of superconducting ring resonators as an initial step toward their implementation in superconducting electronics and quantum technologies, with promising applications including superconducting parametric amplifiers with pump-signal isolation, flux-controlled quantum circuits, ultra-sensitive measurements in quantum sensing, and THz instrumentations. These devices have the potentially valuable property of supporting two orthogonal electromagnetic modes that couple to a common Cooper pair, quasiparticle, and phonon system. We present here a comprehensive theoretical and experimental analysis of the superconducting ring resonator system. We have developed superconducting ring resonator models that describe the key features of microwave behaviour to first order, providing insights into how transmission line inhomogeneities give rise to frequency splitting and mode rotation. Furthermore, we constructed signal flow graphs for a four-port ring resonator to numerically validate the behaviour predicted by our theoretical analysis. Superconducting ring resonators were fabricated in both coplanar waveguide and microstrip geometries using Al and Nb thin films. Microwave characterisation of these devices demonstrates close agreement with theoretical predictions. Our study reveals that frequency splitting and mode rotation are prevalent in ring systems with coupled degenerate modes, and these phenomena become distinctly resolved in high quality factor superconducting ring resonators.