Fano Interference in Microwave Resonator Measurements

TL;DR

This paper investigates how Fano interference affects the accuracy of resonator measurements in microwave experiments, revealing systematic errors in quality factor extraction and proposing methods to characterize and mitigate these effects.

Contribution

It demonstrates the impact of Fano interference on resonator quality factor measurements and provides a way to identify and correct for this interference in experimental setups.

Findings

Fano interference causes systematic errors in $Q_i$ measurements.

Uncertainty in $Q_i$ increases with coupling coefficient.

Methods to characterize and eliminate Fano interference are proposed.

Abstract

Resonator measurements are a simple but powerful tool to characterize a material's microwave response. The losses of a resonant mode are quantified by its internal quality factor $Q_\mathrm{i}$, which can be extracted from the scattering coefficient in a microwave reflection or transmission measurement. Here we show that a systematic error on $Q_\mathrm{i}$ arises from Fano interference of the signal with a background path. Limited knowledge of the interfering paths in a given setup translates into a range of uncertainty for $Q_\mathrm{i}$, which increases with the coupling coefficient. We experimentally illustrate the relevance of Fano interference in typical microwave resonator measurements and the associated pitfalls encountered in extracting $Q_\mathrm{i}$. On the other hand, we also show how to characterize and utilize the Fano interference to eliminate the systematic error.