The scattering coefficients of superconducting microwave resonators: I. Transfer-matrix approach

Abstract

We describe a unified classical approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. To fill the gap between experiment and theory, we also consider the influences of small circuit asymmetry and the finite length of the feedlines, and describe a procedure to correct them in typical measurement results. We show that, similar to the transmission coefficient of a hanger-type resonator, the reflection coefficient of a necklace- or bridge-type resonator does also contain a reference point which can be used to characterize the electrical properties of a microwave resonator in a single step. Our results provide a comprehensive understanding of superconducting microwave resonators from the design concepts to the characterization details.

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Cited by in corpus (7)

• Quantum behavior of a superconducting Duffing oscillator at the dissipative phase transition
• The scattering coefficients of superconducting microwave resonators: II. System-bath approach
• Gate-Compatible Circuit Quantum Electrodynamics in a Three-Dimensional Cavity Architecture
• Compact inductor-capacitor resonators at sub-gigahertz frequencies
• Correlation measurement of propagating microwave photons at millikelvin
• Superconducting Cavity-Based Sensing of Band Gaps in 2D Materials
• Superconducting cavity probes sliding ferroelectricity in small-angle twisted WSe${}_2$