Traceable In Situ Microwave Power Measurement at the Cryogenic Device Plane in a Dilution Refrigerator

Abstract

Accurate knowledge of the microwave power delivered to a cryogenic device under test (DUT) is essential for the characterization and operation of superconducting quantum circuits. However, this information is difficult to obtain inside dilution refrigerators because of distributed attenuation, impedance mismatch, switch-path repeatability, and temperature-dependent microwave components. This paper presents an in situ measurement method for RF power at the cryogenic device plane. The method uses a custom variable temperature stage (VTS) as a cryogenic thermal-transfer element. The TVS is alternately heated by a four-wire DC heater and by microwave power dissipated in a 20 dB pass-through attenuator. By fitting the thermal transients and comparing the corresponding steady-state temperatures, the absorbed microwave power is inferred from a directly measured DC electrical power through an AC/DC substitution procedure. The finite reflection and transmission of the attenuator are then accounted for by cryogenic two-port scattering-parameter measurements based on a switch-assisted Short--Open--Load--Reciprocal calibration, so that the result is referred to the DUT reference plane. The system is demonstrated in a dilution refrigerator with powers between -43 and -58 dBm at the DUT input plane. The demonstrated relative standard uncertainty ranges from about 2% at -43.9 dBm to about 40% at -57.6 dBm. The proposed approach combines thermal RF power transfer, cryogenic S-parameter correction, and uncertainty evaluation in a measurement architecture compatible with quantum-device experiments, providing a practical route toward traceable microwave-power calibration at millikelvin stages.