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arXiv:1212.4427 · Review of Scientific Instruments

In situ broadband cryogenic calibration for two-port superconducting microwave resonators

Jen-Hao Yeh, Steven M. Anlage

Published Mar 1, 2013• 53 citations
arXivHTMLPDF

Abstract

We introduce an improved microwave calibration method for use in a cryogenic environment, based on a traditional three-standard calibration, the Thru-Reflect-Line (TRL) calibration. The modified calibration method takes advantage of additional information from multiple measurements of an ensemble of realizations of a superconducting resonator, as a new pseudo-Open standard, to correct errors in the TRL calibration. We also demonstrate an experimental realization of this in situ broadband cryogenic calibration system utilizing cryogenic switches. All calibration measurements are done in the same thermal cycle as the measurement of the resonator (requiring only an additional 20 min), thus avoiding 4 additional thermal cycles for traditional TRL calibration (which would require an additional 12 days). The experimental measurements on a wave-chaotic microwave billiard verify that the new method significantly improves the measured scattering matrix of a high-quality-factor superconducting resonator.

DOI
10.1063/1.4797461

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We introduce an improved microwave calibration method for use in a cryogenic environment, based on a traditional three-standard calibration, the Thru-Reflect-Line (TRL) calibration. The modified calibration method takes advantage of additional information from multiple measurements of an ensemble of realizations of a superconducting resonator, as a new pseudo-Open standard, to correct errors in the TRL calibration. We also demonstrate an experimental realization of this in situ broadband cryogenic calibration system utilizing cryogenic switches. All calibration measurements are done in the same thermal cycle as the measurement of the resonator (requiring only an additional 20 min), thus avoiding 4 additional thermal cycles for traditional TRL calibration (which would require an additional 12 days). The experimental measurements on a wave-chaotic microwave billiard verify that the new method significantly improves the measured scattering matrix of a high-quality-factor superconducting resonator.
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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.
We are developing a new instrument, the RF Josephson arbitrary waveform synthesizer (RF-JAWS), for communications metrology and quantum information applications. An important aspect of the RF-JAWS design is the accurate and traceable characterization of its superconducting devices. In this article, we present a procedure for characterizing microwave superconducting devices in a cryogenic RF probe station via a vector network analyzer (VNA) calibrated with a custom cryogenic calibration kit colocated with the superconducting device under test (DUT) in the cryogenic environment. By de-embedding lossy and dispersive RF interconnects linking the superconducting DUT to the measurement apparatus at room temperature, we characterize the DUT exactly at the cryogenic on-wafer reference plane. More importantly, we operate our VNA with an external modulated source and our procedure features metrology-grade multiline thru-reflect-line calibration and absolute power and phase corrections, as opposed to the more common relative scattering-parameter correction. In addition, we apply anX-parameter model to account for impedance mismatch in cryogenic Josephson microwave sources. Our techniques are also suitable for cryogenic characterization of microwave superconducting devices for solid-state quantum computers and could help to optimize the quantum-classical interfaces in these systems.
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.
A method is proposed and experimentally explored for in-situ calibration of complex transmission data for superconducting microwave resonators. This cryogenic calibration method accounts for the instrumental transmission response between the vector network analyzer reference plane and the device calibration plane. Once calibrated, the observed resonator response is analyzed in detail by two approaches. The first, a phenomenological model based on physically realizable rational functions, enables the extraction of multiple resonance frequencies and widths for coupled resonators without explicit specification of the circuit network. In the second, an ABCD-matrix representation for the distributed transmission line circuit is used to model the observed response from the characteristic impedance and propagation constant. When used in conjunction with electromagnetic simulations, the kinetic inductance fraction can be determined with this method with an accuracy of 2%. Datasets for superconducting microstrip and coplanar-waveguide resonator devices were investigated and a recovery within 1% of the observed complex transmission amplitude was achieved with both analysis approaches. The experimental configuration used in microwave characterization of the devices and self-consistent constraints for the electromagnetic constitutive relations for parameter extraction are also presented.