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arXiv:2303.02933 · Physical Review Applied

Cryogenic hyperabrupt strontium titanate varactors for sensitive reflectometry of quantum dots

Rafael S. Eggli, Simon Svab, Taras Patlatiuk, Dominique A. Trüssel, Miguel J. Carballido, Pierre Chevalier Kwon, Simon Geyer, Ang Li, Erik P. A. M. Bakkers, Andreas V. Kuhlmann, Dominik M. Zumbühl

Published Nov 28, 2023• 14 citations
arXivHTMLPDF

Abstract

Radio-frequency reflectometry techniques enable high-bandwidth readout of semiconductor quantum dots. Careful impedance matching of the resonant circuit is required to achieve high sensitivity, which, however, proves challenging at cryogenic temperatures. Gallium arsenide--based voltage-tunable capacitors, so-called varactor diodes, can be used for in situ tuning of the circuit impedance but deteriorate and fail at temperatures below 10 K and in magnetic fields. Here, we investigate a varactor based on strontium titanate with a hyperabrupt capacitance-voltage characteristic, i.e., a capacitance tunability similar to the best gallium arsenide--based devices. The varactor design introduced here is compact, scalable, and easy to wire bond, with an accessible capacitance range from 45 pF to 3.2 pF. We tune a resonant inductor-capacitor circuit to perfect impedance matching and observe robust temperature- and field-independent matching down to 11 mK and up to 2 T in-plane field. Finally, we perform gate-dispersive charge sensing on a germanium-silicon core-shell nanowire hole double quantum dot, paving the way toward gate-based single-shot spin readout. Our results bring small magnetic field--resilient highly tunable varactors to mK temperatures, expanding the toolbox of cryo-radio-frequency applications.

DOI
10.1103/physrevapplied.20.054056

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Radio-frequency reflectometry techniques enable high-bandwidth readout of semiconductor quantum dots. Careful impedance matching of the resonant circuit is required to achieve high sensitivity, which, however, proves challenging at cryogenic temperatures. Gallium arsenide--based voltage-tunable capacitors, so-called varactor diodes, can be used for in situ tuning of the circuit impedance but deteriorate and fail at temperatures below 10 K and in magnetic fields. Here, we investigate a varactor based on strontium titanate with a hyperabrupt capacitance-voltage characteristic, i.e., a capacitance tunability similar to the best gallium arsenide--based devices. The varactor design introduced here is compact, scalable, and easy to wire bond, with an accessible capacitance range from 45 pF to 3.2 pF. We tune a resonant inductor-capacitor circuit to perfect impedance matching and observe robust temperature- and field-independent matching down to 11 mK and up to 2 T in-plane field. Finally, we perform gate-dispersive charge sensing on a germanium-silicon core-shell nanowire hole double quantum dot, paving the way toward gate-based single-shot spin readout. Our results bring small magnetic field--resilient highly tunable varactors to mK temperatures, expanding the toolbox of cryo-radio-frequency applications.
Radio-frequency reflectometry allows for fast and sensitive electrical readout of charge and spin qubits hosted in quantum dot devices coupled to resonant circuits. Optimizing readout, however, requires frequency tuning of the resonators and impedance matching. This is difficult to achieve using conventional semiconductor or ferroelectric-based varactors in the detection circuit as their performance degrades significantly in the mK temperature range relevant for solid-state quantum devices. Here we explore a different type of material, strontium titanate, a quantum paraelectric with exceptionally large field-tunable permittivity at low temperatures. Using strontium titanate varactors we demonstrate perfect impedance matching and resonator frequency tuning at 6 mK and characterize the varactors at this temperature in terms of their capacitance tunability, dissipative losses and magnetic field sensitivity. We show that this allows us to optimize the radio-frequency readout signal-to-noise ratio of carbon nanotube quantum dot devices to achieve a charge sensitivity of 4.8 μμμe/Hz1/2^{1/2}1/2 and capacitance sensitivity of 0.04 aF/Hz1/2^{1/2}1/2.
Abstract Radiofrequency reflectometry can provide fast and sensitive electrical read-out of charge and spin qubits in quantum dot devices coupled to resonant circuits. In situ frequency tuning and impedance matching of the resonator circuit using voltage-tunable capacitors (varactors) is needed to optimize read-out sensitivity, but the performance of conventional semiconductor- and ferroelectric-based varactors degrades substantially in the millikelvin temperature range relevant for solid-state quantum devices. Here we show that strontium titanate and potassium tantalate, materials which can exhibit quantum paraelectric behaviour with large field-tunable permittivity at low temperatures, can be used to make varactors with perfect impedance matching and resonator frequency tuning at 6 mK. We characterize the varactors at 6 mK in terms of their capacitance tunability, dissipative losses and magnetic field insensitivity. We use the quantum paraelectric varactors to optimize the radiofrequency read-out of carbon nanotube quantum dot devices, achieving a charge sensitivity of 4.8 μe Hz−1/2 and a capacitance sensitivity of 0.04 aF Hz−1/2.
Electrical readout of spin qubits requires fast and sensitive measurements, which are hindered by poor impedance matching to the device. We demonstrate perfect impedance matching in a radio-frequency readout circuit, using voltage-tunable varactors to cancel out parasitic capacitances. An optimized capacitance sensitivity of 1.6 aF/√Hz is achieved at a maximum source-drain bias of 170−μV root-mean-square and with a bandwidth of 18 MHz. Coulomb blockade in a quantum-dot is measured in both conductance and capacitance, and the two contributions are found to be proportional as expected from a quasistatic tunneling model. We benchmark our results against the requirements for single-shot qubit readout using quantum capacitance, a goal that has so far been elusive.
Quantum computing has emerged as a promising technology for next-generation information processing, utilizing semiconductor quantum dots as one of the candidates for quantum bits. Radio-frequency (rf) reflectometry plays an important role in the readout of quantum dots but requires a precise rf measurement technique at cryogenic temperatures. While cryogenic calibration techniques, essential for rf reflectometry, have been developed, on-board calibration near the device remains an important challenge. In this study, we develop an on-board calibrated rf measurement system operating at 4 K for characterizing SrTiO3-based varactors, which are promising components for tunable impedance matching circuits. Our system enables accurate measurements by eliminating errors associated with long rf circuit lines. We investigate the effects of annealing conditions, crystal orientation, and Ca doping of SrTiO3 crystals on the varactor properties in the frequency range for rf reflectometry. Our results provide insights for optimizing these components for cryogenic rf applications in quantum information processing systems.
We present a sensitive, tunable radio-frequency resonator designed to detect reactive changes in nanoelectronic devices down to dilution refrigerator temperatures. The resonator incorporates GaAs varicap diodes to allow electrical tuning of the resonant frequency and the coupling to the input line. We find a resonant frequency tuning range of 8.4 MHz at 55 mK that increases to 29 MHz at 1.5 K. To assess the impact on performance of different tuning conditions, we connect a quantum dot in a silicon nanowire field-effect transistor to the resonator and measure changes in the device capacitance caused by cyclic electron tunneling. At 250 mK, we obtain an equivalent charge sensitivity of 43 μe/Hz when the resonator and the line are impedance-matched and show that this sensitivity can be further improved to 31 μe/Hz by re-tuning the resonator. We understand this improvement by using an equivalent circuit model and demonstrate that for maximum sensitivity to capacitance changes, in addition to impedance matching, a high-quality resonator with low parasitic capacitance is desired.
This paper reports on the extraction of the equivalent circuit model parameters of a physically defined silicon quantum dot at a cryogenic temperature and design of the impedance matching circuits to improve the performance of a charge sensor for radio-frequency (RF) reflectometry. The I-V characteristics and the S-parameters of the quantum dot device are measured around a Coulomb peak at 4.2 K. The measured results are modeled by an RC parallel circuit, and the model parameters for the quantum dot device were obtained. We consider three impedance matching circuits for RF reflectometry of a quantum dot: shunt capacitor-series inductor type, shunt inductor-series capacitor type, and shunt inductor-series inductor-type. We formulate and compare the sensitivity and bandwidth of RF reflectometry for the three types of circuits. The analysis should be useful for selecting the optimal matching circuit and the circuit parameters for given equivalent circuit parameters and working frequency. This procedure is demonstrated for a quantum dot with the characterized model circuit along with simulated performance. This design technique of matching circuit for RF reflectometry can be applied to any device that can be represented by an RC parallel circuit. These results will facilitate to realize fast semiconductor qubit readout in various quantum dot platforms.