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arXiv:2103.01491 · Quantum Science and Technology

Cryogenic single-port calibration for superconducting microwave resonator measurements

H. Wang, Suren Singh, Corey Rae McRae, Joseph C. Bardin, S-X Lin, Nizar Messaoudi, Alessandro R. Castelli, Yaniv Jacob Rosen, E T Holland, D. P. Pappas, J. Mutus

Published Jun 1, 2021• 34 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/2058-9565/ac070e

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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.
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.
Superconducting qubits, though promising for both near-term problem-solving as well as the development of large-scale quantum computing systems, are limited in performance largely by materials-induced decoherence channels which are maximized at millikelvin temperatures, single photon powers, and microwave frequencies. Superconducting microwave resonators are ideal tools for measuring these materials losses due to their simplicity, well-understood behavior, and sensitivity to these same losses. In order to better understand and mitigate dominant qubit decoherence channels, accurate and precise characterization of superconducting microwave resonator performance is critical. In this paper, current measurement techniques for superconducting microwave resonators are discussed, including experimental set-up, error analysis, and cryogenic calibration of a vector network analyzer.
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.
In the field of quantum information science, superconducting quantum integrated circuits are operated at millikelvin temperatures inside dilution refrigerators. The microwave performance of such non-connectorised devices can be characterised by measuring their calibrated S-parameters. The design of high-quality microwave standards is essential to achieve accurate calibration. In this work we describe the architecture of a full 2-port S-parameter measurement set-up for use at millikelvin temperatures along with the microwave calibration unit. The design of the standards for use in the calibration unit at millikelvin temperatures is described and verified using electromagnetic simulation and measurements. The suitability of the standards is verified by characterising a commercial attenuator as a test device.
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.
The performance of superconducting circuits for quantum computing is limited by materials losses. In particular, coherence times are typically bounded by two-level system (TLS) losses at single photon powers and millikelvin temperatures. The identification of low loss fabrication techniques, materials, and thin film dielectrics is critical to achieving scalable architectures for superconducting quantum computing. Superconducting microwave resonators provide a convenient qubit proxy for assessing performance and studying TLS loss and other mechanisms relevant to superconducting circuits such as non-equilibrium quasiparticles and magnetic flux vortices. In this review article, we provide an overview of considerations for designing accurate resonator experiments to characterize loss, including applicable types of losses, cryogenic setup, device design, and methods for extracting material and interface losses, summarizing techniques that have been evolving for over two decades. Results from measurements of a wide variety of materials and processes are also summarized. Finally, we present recommendations for the reporting of loss data from superconducting microwave resonators to facilitate materials comparisons across the field.