Cryogenic single-port calibration for superconducting microwave resonator measurements

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