An analysis method for asymmetric resonator transmission applied to superconducting devices

TL;DR

This paper introduces the Diameter Correction Method (DCM) for accurately analyzing asymmetric resonance line shapes in superconducting microwave resonators, improving upon the conventional $$ Rotation Method ($$RM) especially under high asymmetry conditions.

Contribution

The paper derives a general analytical model for asymmetric resonance line shapes and proposes the DCM, which corrects overestimations of internal quality factor by the traditional method.

Findings

DCM accurately extracts $Q_i$ in asymmetric conditions.

$$RM overestimates $Q_i$ with high asymmetry.

Analytical and numerical validation of DCM effectiveness.

Abstract

We examine the transmission through nonideal microwave resonant circuits. The general analytical resonance line shape is derived for both inductive and capacitive coupling with mismatched input and output transmission impedances, and it is found that for certain non-ideal conditions the line shape is asymmetric. We describe an analysis method for extracting an accurate internal quality factor ($Q_i$), the Diameter Correction Method (DCM), and compare it to the conventional method used for millikelvin resonator measurements, the $\phi$ Rotation Method ($\phi$RM). We analytically find that the $\phi$RM deterministically overestimates $Q_i$ when the asymmetry of the resonance line shape is high, and that this error is eliminated with the DCM. A consistent discrepancy between the two methods is observed when they are used to analyze both simulations from a numerical linear solver and data from asymmetric coplanar superconducting thin-film resonators.