Low-temperature tunable radio-frequency resonator for sensitive dispersive readout of nanoelectronic devices

Abstract

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 impedancematched 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.High-frequency reflectometry is a technique widely used to study the dynamical properties of nanoelectronic devices due to its enhanced sensitivity and large bandwidth when compared to direct current measurements 1,2 . By embedding a device in an electrical resonator, resistive or reactive changes in the device can be inferred from the resonator's response.Previous work has shown that, for sensitive detection of resistive changes, good impedance matching between the high frequency line and the resonator, as well as large fractional changes in resistance, are paramount 3,4 . Tunable resonators have recently been explored for sensitive capacitance readout 5,6 , concluding that optimal sensitivity occurs when the resonator is impedance matched to the line. In this Letter, we extend the work of Ares et al. and demonstrate that for maximal sensitivity to capacitance changes, in addition to an optimally matched resonator, large fractional changes in capacitance and a high internal-Q resonator are essential. We focus on dispersive changes because, for quantum computing technologies, measurement via detection of reactive changes is preferred since it allows for quantum-limited measurements of the qubits 7-9 .To achieve this, we present a tunable high-frequency resonator that remains operational at the base temperature of a dilution refrigerator and allows matching to be achieved at 200 mK. In previous reports, impedance matching was limited to temperatures of 1 K and above 5,10 . We couple our resonator to a quana) david.ibberson@bristol.ac.uk b) mg507@cam.ac.uk tum dot (QD) in a silicon nanowire field-effect transistor (NWFET) and measure changes in the device capacitance due to adiabatic single-electron tunneling events. We observe that sensitive detection of capacitance changes relies on an optimal balance of maximum power transfer to the resonator, maximal internal quality factor and minimized resonator capacitance, and that all three paramet...

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