Cryogenic single-port calibration for superconducting microwave resonator 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 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.

Surface acoustic wave resonators on thin film piezoelectric substrates in the quantum regime

“…The SAW resonators are investigated by microwave spectroscopy in a dilution refrigerator with a base temperature of T base ≈ 20 mK. Specifically, we measure the complex microwave reflection amplitude S 11 (f) using a vector network analyzer (see [37]). The microwave input signal is attenuated at the different temperature stages with a total of 66 dB attenuation which allows to probe our SAW resonators at the single excitation limit (as discussed in more detail below).…”

Surface acoustic wave resonators on thin film piezoelectric substrates for quantum acoustics

“…Ref. [34]). The microwave input signal is attenuated at the different temperature stages with a total of 66 dB attenuation which allows to probe our SAW resonators at the single excitation limit (as discussed in more detail below).…”

Validating S‐parameter measurements of RF integrated circuits at milli‐Kelvin temperatures

“…In order to precisely characterise the S-parameters of RF components at mK temperatures, a calibration scheme that shifts the reference planes of the measurement to the ends of the device under test (DUT) needs to be implemented [3], thus de-embedding the intervening components up to the ports of the vector network analyser (VNA), operating at room temperature. Some previous work has been demonstrated for calibrated measurements of two-port RF components at mK temperatures [4][5][6][7][8]. When developing new metrology capabilities, it is important to validate the measurements by comparing and verifying the measurement results obtained using independent measurement methods, through interlaboratory comparisons and through comparison of measurement results obtained using different calibration techniques.…”

“…When developing new metrology capabilities, it is important to validate the measurements by comparing and verifying the measurement results obtained using independent measurement methods, through interlaboratory comparisons and through comparison of measurement results obtained using different calibration techniques. The measurements results discussed in [4][5][6][7][8] relied on using a single calibration technique and comparisons of the measurement results were not made using multiple independent calibration techniques, which is important in order to validate the measurements, when developing quality assured metrology capabilities at mK temperatures, to provide confidence in the measurements [9].…”