Cryogenic single-port calibration for superconducting microwave resonator measurements

TL;DR

This paper presents a data-based single-port calibration method for superconducting microwave resonator measurements at cryogenic temperatures, enabling accurate extraction of quality factors in quantum experiments.

Contribution

It introduces a novel calibration technique using commercial standards and VNA at millikelvin temperatures, validated against traditional two-port methods.

Findings

Calibration method accurately extracts quality factors

Validated against established two-port techniques

Applicable for quantum phenomena measurements

Abstract

Superconducting circuit testing and materials loss characterization requires robust and reliable methods for the extraction of internal and coupling quality factors of microwave resonators. A common method, imposed by limitations on the device design or experimental configuration, is the single-port reflection geometry, i.e. reflection-mode. However, impedance mismatches in cryogenic systems must be accounted for through calibration of the measurement chain while it is at low temperatures. In this paper, we demonstrate a data-based, single-port calibration using commercial microwave standards and a vector network analyzer (VNA) with samples at millikelvin temperature in a dilution refrigerator, making this method useful for measurements of quantum phenomena. Finally, we cross reference our data-based, single-port calibration and reflection measurement with over-coupled 2D- and 3D-resonators against well established two-port techniques corroborating the validity of our method.