Fano Interference in Microwave Resonator Measurements

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.

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