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Review of Scientific Instruments

Two-port microwave calibration at millikelvin temperatures

Leonardo Ranzani, Lafe Spietz, Zoya B. Popovic, José Aumentado

Published Mar 1, 2013• 84 citations
Publisher

Abstract

In this work we introduce a system for 2-port microwave calibration at millikelvin temperatures operating at the coldest stage of a dilution refrigerator by use of an adapted thru-reflect-line algorithm. We show that this can be an effective tool for characterizing common 50 Ω microwave components with better than 0.1 dB accuracy at temperatures that are relevant to many current experiments in superconducting quantum information.

DOI
10.1063/1.4794910

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In this work we introduce a system for 2-port microwave calibration at millikelvin temperatures operating at the coldest stage of a dilution refrigerator by use of an adapted thru-reflect-line algorithm. We show that this can be an effective tool for characterizing common 50 Ω microwave components with better than 0.1 dB accuracy at temperatures that are relevant to many current experiments in superconducting quantum information.
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.
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 report calibrated microwave transmission and reflection measurements of a qubit sample holder at millikelvin temperatures. The methodology we present extends our previous work on one-port cryogenic short-open-load (SOL) calibration to a two-port SOLT measurement by implementing an unknown thru (T) standard. We report the resulting calibrated transmission and reflection at millikelvin temperatures through a printed circuit board that is installed into the sample holder. Finally, we consider a cascade of components at the end of a qubit drive line that includes (1) a cryogenic attenuator, (2) a coaxial cable, and (3) a qubit sample holder. Using experimentally determined parameters for return losses for all three components, we calculate the negligible state-preparation error in the frequency band of 5-7 GHz due to control pulse distortions arising from reflection at the coaxial launches. Taken together, our results highlight the utility of calibrated cryogenic scattering parameter measurements for the validation of qubit packaging and the wiring in its immediate vicinity.
Development of RF and microwave metrology capabilities at cryogenic temperatures is critical for the development of high-performance microwave devices to facilitate commercialization of cryogenic quantum technologies. This article presents a broadband microwave S-parameter calibration scheme suitable for cryogenic environments operating at temperatures down to tens of milli-kelvin (mK). The technique is based on a weighted multi-line thru-reflect-line (TRL) calibration approach and is demonstrated using coaxial air line calibration standards. One-and two-port microwave devices commonly used in cryogenic quantum computing applications, a cryogenic 50 Ω~\Omega Ωmatched load and a cryogenic 6 dB attenuator, were measured. The measured results at mK temperatures indicate that when combined with calibration standards of appropriate electrical length, the weighted multi-line TRL calibration scheme allows broadband frequency coverage compared to conventional TRL calibration schemes utilizing a single line standard. The mechanical and electrical properties of the line standards at mK temperatures were investigated and discussed. These findings establish the feasibility of utilizing multiple off-the-shelf coaxial air lines to enhance the frequency range of calibrations at mK temperatures.
In this work, we characterize the 2-port scattering parameters of a superconducting quantum interference device amplifier at ∼20 mK over several gigahertz of bandwidth. The measurement reference plane is positioned on a 6.25 Ω microstrip line situated directly at the input and output of the device by means of a thru-reflect-line cryogenic calibration procedure. From the scattering parameters, we derive the device available power gain, isolation, and input impedance over the 2–8 GHz range. This measurement methodology provides a path towards designing wide-band matching circuits for low impedance superconducting amplifiers operating at dilution refrigerator temperatures.
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.