Nongalvanic Calibration and Operation of a Quantum Dot Thermometer

Abstract

A cryogenic quantum dot thermometer is calibrated and operated using only a single non-galvanic gate connection. The thermometer is probed with radio-frequency reflectometry and calibrated by fitting a physical model to the phase of the reflected radio-frequency signal taken at temperatures across a small range. Thermometry of the source and drain reservoirs of the dot is then performed by fitting the calibrated physical model to new phase data. The thermometer can operate at the transition between thermally broadened and lifetime broadened regimes, and outside the temperatures used in calibration. Electron thermometry was performed at temperatures between 3.0 K and 1.0 K, in both a 1 K cryostat and a dilution refrigerator. In principle, the experimental setup enables fast electron temperature readout with a sensitivity of 4.0 ± 0.3 mK/ √ Hz, at kelvin temperatures. The non-galvanic calibration process gives a readout of physical parameters, such as the quantum dot lever arm. The demodulator used for reflectometry readout is readily available and very affordable.

Radio-Frequency Coulomb-Blockade Thermometry

“…This is straightforward but in standard dc or quasi-dc measurements, it typically takes several minutes in order to reach satisfactory accuracy in thermometry. Another option to measure the conductance is to monitor either the reflectance or the conductance in a resonant circuit, with the device under study embedded [15][16][17][18]. In this letter, we propose and demonstrate experimentally an rf transmission measurement of a CBT, where similar accuracy is achieved in less than 1 s. The transmitted microwave power is related to the conductance in a simple linear way, making the analysis and the determination of temperature from the measured signal straightforward.…”

Fast Thermodynamic Study on a Silicon Nanotransistor at Cryogenic Temperatures

“…35 However, improvements in temperature sensitivity are still needed by addressing measurement noise. 33 In this study, we investigate the temperature variation and thermodynamics of a silicon nanotransistor induced by laser pulses. Leveraging RF-reflectometry, we investigate the temperature variation on a submillisecond time scale governed by the thermal gradients associated with the device during and after the laser pulses across various pulse lengths and powers.…”

“…When an RF signal is applied to the source of the FinFET, hole tunnelling occurs periodically between the QD and the reservoir, creating a load for the RF signal that directly depends on P QD . In general, the load can have both dissipative and dispersive components, ,,, but we focus on the dispersive load, which uses the quantum capacitance associated with the hole tunnelling for temperature analysis. The quantum capacitance C q can be expressed as C normalq = e α ∂ P normalQ normalD ∂ V normalg = α 2 e 2 4 k normalB T normalh cosh − 2 ( e α false( V normalg − V normalg 0 false) 2 k B T h ) where α is the gate lever arm of the QD level.…”

“…In a previous study, a 128-fold ensemble-averaged signal was utilized to generate a noise spectrum which reveals a sensitivity of approximately 11 mK/ normalH normalz at 3 K. However, this ensemble-averaging approach is incompatible with continuous temperature measurement. For comparison purposes only, the same ensemble-averaging is applied to our signal, yielding a sensitivity of approximately 0.3 mK/ normalH normalz at 3.9 K. This represents a 60-fold improvement compared to the previous result at 3 K . The sensitivity is 1 order of magnitude smaller than the 4 mK/ normalH normalz sensitivity obtained without ensemble-averaging, as expected due to the reduction of uncorrelated measurement noise through signal averaging (see Supporting Information section 7.…”

Quantum Dot-Based Parametric Amplifiers

“…Beyond JJs, another non-linear reactive element that manifests in low-dimensional systems is quantum capacitance: rapid variations of the number of states with respect to the Fermi energy can generate an additional differential capacitance that is dual of the Josephson inductance [25,26]. The applications of quantum capacitance in artificial two-level systems, such as the Cooper-pair box or semiconductor quantum dots (QDs), have been primarily oriented towards compact, high-fidelity quantum state readout [27][28][29] and low-temperature thermometry [30,31]. However, since tunnelling can be designed to be adiabatic, quantum capacitance devices may provide an alternative dissipation-less element for parametric amplification [32].…”