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arXiv:2012.01209 · Physical Review Applied

Nongalvanic Calibration and Operation of a Quantum Dot Thermometer

Joshua Chawner, Sylvain Barraud, M. Fernando González-Zalba, S. Holt, Edward A. Laird, Yu. A. Pashkin, Jonathan R. Prance

Published Mar 16, 2021• 15 citations
arXivHTMLPDF

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 $3.0\,\mathrm{K}$ and $1.0\,\mathrm{K}$, in both a $1\,\mathrm{K}$ cryostat and a dilution refrigerator. The experimental setup allows fast electron temperature readout with a sensitivity of $4.0\pm0.3 \, \mathrm{mK}/\sqrt{\mathrm{Hz}}$, 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.

DOI
10.1103/physrevapplied.15.034044

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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 K3.0\,\mathrm{K}3.0K and 1.0 K1.0\,\mathrm{K}1.0K, in both a 1 K1\,\mathrm{K}1K cryostat and a dilution refrigerator. The experimental setup allows fast electron temperature readout with a sensitivity of 4.0±0.3 mK/Hz4.0\pm0.3 \, \mathrm{mK}/\sqrt{\mathrm{Hz}}4.0±0.3mK/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.
The performance and accuracy of quantum electronics is substantially degraded when the temperature of the electrons in the devices is too high. The electron temperature can be reduced with appropriate thermal anchoring and by filtering both the low frequency and radio frequency noise. Ultimately, for high performance filters the electron temperature can approach the phonon temperature (as measured by resistive thermometers) in a dilution refrigerator. In this application note, the method for measuring the electron temperature in a typical quantum electronics device using Coulomb blockade thermometry is described. This technique is applied to find the readily achievable electron temperature in the device when using the QFilter provided by QDevil. With our thermometry measurements, using a single GaAs/AlGaAs quantum dot in an optimized experimental setup, we determined an electron temperature of 28 ±\pm± 2 mK for a dilution refrigerator base temperature of 18 mK.
Cryogenic temperatures are crucial for the operation of semiconductor quantum electronic devices, yet the heating effects induced by microwave or laser signals used for quantum state manipulation can lead to significant temperature variations at the nanoscale. Therefore, probing the temperature of individual devices in working conditions and understanding the thermodynamics are paramount for designing and operating large-scale quantum computing systems. In this study, we demonstrate high-sensitivity fast thermometry in a silicon nanotransistor at cryogenic temperatures using RF reflectometry. Through this method, we explore the thermodynamic processes of the nanotransistor during and after a laser pulse and determine the dominant heat dissipation channels in the few-kelvin temperature range. These insights are important to understand thermal budgets in quantum circuits, with our techniques being compatible with microwave and laser radiation, offering a versatile approach for studying other quantum electronic devices in working conditions.
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.
Radio frequency (RF) reflectometry is a well understood measurement technique in common use by RF engineers today. This technique has been applied at low temperature to probe the impedance of nanoscale devices for over two decades. These measurements typically employ basic resonant impedance transformers to bring the device impedance close to the characteristic impedance of the measurement apparatus. In 2013 it was discovered by Colless et al. that reflectometry could be used to measure extremely small impedance changes in a gate coupled to a quantum dot to directly probe the charge state of the dot. This has simplified measurements of certain nanoscale devices including single electron boxes (SEBs) and semiconductor qubits. Despite the maturity of RF reflectometry measurements in general, researchers working at low temperature continue to make basic mistakes in their measurements. The root cause of most of these mistakes is the failure to properly calibrate the measurement apparatus. In some cases this leads researchers to unrealistic conclusions when trying to match measurements to theory. This dissertation demonstrates that a low temperature RF calibration can be very easy and straightforward using inexpensive, off the shelf SMA terminators as calibration standards. A proper calibration allows for direct quantitative comparisons between data measured on different reflectometers or between data and simulations. The consistency between measurements and simulations then allows for straightforward design and implementation of improved impedance transformers, increasing the SNR of extremely sensitive measurements, with simple data-based simulations. A new type of single electron device, the capacitively coupled RF single electron transistor (CSET) is proposed and demonstrated which can rival the traditional RF SET in sensitivity but integrates more effectively into arrays and may offer a level of resistance to electrostatic discharge damage.
Thousands to millions of sensitive signals will need to be conveyed through all the temperature stages of a dilution fridge to operate future large-scale quantum processors made of many quantum bits. The exploding number of heat-conductive coaxial cables will overwhelm the fridge cooling capabilities, detrimental to the quantum core. Moving the control electronics down to cryogenic temperatures allows the use of already-available superconducting cables, alleviating heat conduction between low-temperature stages, and appears as a clear path towards scalability in the number of operating qubits.This Ph.D. work aimed to explore the use of the industrial CMOS 28nm Fully-Depleted Silicon-On-Insulator (FD-SOI) technology at cryogenic temperatures for quantum computing applications. Our first objective is to extend the sparse existing knowledge about the FD-SOI 28nm transistors at cryogenic temperatures for practical aspects of circuit design and later for developments of compact models.To speed-up the characterization of single devices with the inherent hour-long cooling cycles, we designed an integrated circuit multiplexing a thousand of transistors for different geometries and gate-stack flavors for low-frequency measurement of the current-voltage characteristics and pair-matching analysis from 300 down to 0.1K. We discuss and analyze the evolution trends with varying geometry at different temperatures for important quantities in circuit design, such as the transconductance, the conductance, and the transconductance over drain current ratio of individual transistors.Secondly, we explore the low-temperature co-integration and the full on-chip integration of semiconductor quantum devices with classical electronics aimed at specific measurements down to the millikelvin range.We first focus on the sub-nanoampere current measurement of quantum dot devices by designing and characterizing a low-power transimpedance amplifier (TIA). The high-gain amplifier is successfully applied to measure the current across single- and double quantum-dot devices, respectively wire-bonded a few mm away or on-chip integrated a few micrometers-away. To further leverage the integration into the same substrate, we connected GHz-range voltage-controlled oscillators to one of the gates of the double dot in an attempt to observe discrete charge pumping in a fully-integrated device.Lastly, we tackled the measurement of the gate capacitance of single quantum devices by proposing a new measurement scheme making use of the cryogenic electronics capabilities as an alternative to the well-known reflectometry. By integrating a voltage-controlled current excitation and a voltage-sensing amplifier in the 200 MHz range, both in close proximity to the quantum device connected to an LC tank, the read-out circuitry of a variation in the device capacitance becomes a purely lumped-element system with impedance measurement of the resonant circuit without any wave propagation like in reflectometry. This approach increases simplicity and compactness of the measurement set-up. We even replace the bulky passive inductor used in reflectometry by an active inductor made of transistors and capacitors, offering improved scalability with a 3-orders of magnitude lower area for the same inductance. The resulting circuit successfully measured aF-capacitance variations of nanometric transistors at 4.2K revealing oscillatory quantum effects in the gate capacitance as a function of the gate and back-gate voltages.At the end of this dissertation, a picture is given with the challenges laying ahead related to circuit architecture and design for the ultimate goal of entering into the era of large-scale quantum processing.
Cryogen-free dilution refrigerators (dry fridges) have become an increasingly popular solution to researchers’ cryogenic measurement needs due to their user friendliness and long term use cost savings (4He does not need to be replenished). However, commercially available dry fridges frequently have an effective electron temperatures much warmer than the base temperature of the mixing chamber of the dry fridge. This thesis documents efforts taken to reduce the electron temperature in a dry fridge and the direct probing of the electron temperature via Coulomb blockade thermometry in a 500 nm wide quantum dot.