Radio-frequency Reflectometry Research Articles

Quantum paraelectric varactors for radiofrequency measurements at millikelvin temperatures

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.

Development of a high-frequency dielectric spectrometer using a portable vector network analyzer

A simple and novel setup for high-frequency dielectric spectroscopy of materials has been developed using a portable vector network analyzer. The measurement principle is based on radio frequency reflectometry, and both its capabilities and limitations are discussed. The results obtained on a typical liquid crystal prove that the device can provide reliable spectra between 107 and 109 Hz, thus extending the capabilities of conventional impedance analyzers.

Load Cell Based on Binocular Test Body and SAW Strain Sensor With a Radio Frequency Reflectometry Read-Out System

Load Cell Based on Binocular Test Body and SAW Strain Sensor With a Radio Frequency Reflectometry Read-Out System

Wide dynamic range charge sensor operation by high-speed feedback control of radio-frequency reflectometry

Semiconductor quantum dots are useful for controlling and observing quantum states and can also be used as sensors for reading out quantum bits and exploring local electronic states in nanostructures. However, challenges remain for the sensor applications, such as the trade-off between sensitivity and dynamic range and the issue of instability due to external disturbances. In this study, we demonstrate proportional-integral-differential feedback control of the radio-frequency reflectometry in GaN nanodevices using a field-programmable gate array. This technique can maintain the operating point of the charge sensor with high sensitivity. The system also realizes a wide dynamic range and high sensor sensitivity through the monitoring of the feedback signal. This method has potential applications in exploring dynamics and instability of electronic and quantum states in nanostructures.

Dispersive readout of a silicon quantum device using an atomic force microscope-based rf gate sensor

We demonstrate dispersive charge sensing of Si/SiGe single and double quantum dots by coupling sub-micron floating gates to a radio frequency reflectometry (rf-reflectometry) circuit using the tip of an atomic force microscope. Charge stability diagrams are obtained in the phase response of the reflected rf signal. We demonstrate single-electron dot-to-lead and dot-to-dot charge transitions with a signal-to-noise ratio (SNR) of 2 and integration time of τ=2.7 ms and τ=6.4 ms, respectively. The charge sensing SNR compares favorably with results obtained on conventional devices. Moreover, the small size of the floating gates largely eliminates the coupling to parasitic charge traps that can complicate the interpretation of the dispersive charge sensing data.

Measurements of variable capacitance using single port radio frequency reflectometry

A radio frequency (RF) reflectometry technique is presented to measure device capacitances using a probe station. This technique is used to characterize micro-electromechanical system (MEMS) variable capacitor devices that can be connected to create pull-up and pull-down networks used in digital gates for reversible computing. Adiabatic reversible computing is a promising approach to energy-efficient computing that can dramatically reduce heat dissipation by switching circuits at speeds below their RC time constants, introducing a trade-off between energy and speed. The variable capacitors in this study will be measured using single port RF reflectometry achieved with a custom-made RF probe. The RF probe consists of a micromanipulator with an on-board matching network and is calibrated by measuring a capacitive bank that shows a clearly visible frequency shift with the increase in capacitance. The RF probe worked well when measuring static capacitors with no parasitic resistance; however, the frequency shift is masked when measuring the MEMS variable capacitors due to their high in-series parasitic resistance (around 80 kΩ). Therefore, RF reflectometry has the potential to measure MEMS variable capacitors in the range of 0–30 fF when not masked by a high in-series parasitic resistance, creating a fast and versatile method for characterizing variable capacitors that can be used in energy-efficient computing.

Radio frequency cantilever-free scanning probe microscopy

Cantilever-free scanning probe microscopy has enormous potential for high-throughput topography imaging using parallel probe arrays. However, the current imaging mechanism of the cantilever-free tip architecture hardly considers the efficiency of the detection method regarding precision and bandwidth, which could be a bottleneck to expanding the application of this measurement system. In this communication, we present a contact resistance-based cantilever-free imaging system using radio frequency (RF) reflectometry. RF reflectometry measurements provide sensitive detection of the contact resistance with a wide bandwidth, enabling sub-micrometer-scale topography imaging. We demonstrated our imaging system using a carbon black-polydimethylsiloxane composite tip with a custom-built RF reflectometry setup. The proof-of-concept system achieved a resolution of 230 nm and a bandwidth of the detection system of approximately 8.5 MHz, validating the feasibility of the imaging technique for potential high-throughput cantilever-free scanning probe microscopy.

Photoionisation detection of a single Er3+ ion with sub-100-ns time resolution.

Efficient detection of single optical centres in solids is essential for quantum information processing, sensing and single-photon generation applications. In this work, we use radio-frequency (RF) reflectometry to electrically detect the photoionisation induced by a single Er3+ ion in Si. The high bandwidth and sensitivity of the RF reflectometry provide sub-100-ns time resolution for the photoionisation detection. With this technique, the optically excited state lifetime of a single Er3+ ion in a Si nano-transistor is measured for the first time to be [Formula: see text]s. Our results demonstrate an efficient approach for detecting a charge state change induced by Er excitation and relaxation. This approach could be used for fast readout of other single optical centres in solids and is attractive for large-scale integrated optical quantum systems thanks to the multi-channel RF reflectometry demonstrated with frequency multiplexing techniques.

Electromagnetic Sensing Techniques for Monitoring Atopic Dermatitis-Current Practices and Possible Advancements: A Review.

Atopic dermatitis (AD) is one of the most common skin disorders, affecting nearly one-fifth of children and adolescents worldwide, and currently, the only method of monitoring the condition is through an in-person visual examination by a clinician. This method of assessment poses an inherent risk of subjectivity and can be restrictive to patients who do not have access to or cannot visit hospitals. Advances in digital sensing technologies can serve as a foundation for the development of a new generation of e-health devices that provide accurate and empirical evaluation of the condition to patients worldwide. The goal of this review is to study the past, present, and future of AD monitoring. First, current medical practices such as biopsy, tape stripping and blood serum are discussed with their merits and demerits. Then, alternative digital methods of medical evaluation are highlighted with the focus on non-invasive monitoring using biomarkers of AD-TEWL, skin permittivity, elasticity, and pruritus. Finally, possible future technologies are showcased such as radio frequency reflectometry and optical spectroscopy along with a short discussion to provoke research into improving the current techniques and employing the new ones to develop an AD monitoring device, which could eventually facilitate medical diagnosis.

Evaluation of a physically defined silicon quantum dot for design of matching circuit for RF reflectometry charge sensing

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.

Probing quantum devices with radio-frequency reflectometry

Many important phenomena in quantum devices are dynamic, meaning that they cannot be studied using time-averaged measurements alone. Experiments that measure such transient effects are collectively known as fast readout. One of the most useful techniques in fast electrical readout is radio-frequency reflectometry, which can measure changes in impedance (both resistive and reactive) even when their duration is extremely short, down to a microsecond or less. Examples of reflectometry experiments, some of which have been realized and others so far only proposed, include projective measurements of qubits and Majorana devices for quantum computing, real-time measurements of mechanical motion, and detection of non-equilibrium temperature fluctuations. However, all of these experiments must overcome the central challenge of fast readout: the large mismatch between the typical impedance of quantum devices (set by the resistance quantum) and of transmission lines (set by the impedance of free space). Here, we review the physical principles of radio-frequency reflectometry and its close cousins, measurements of radio-frequency transmission and emission. We explain how to optimize the speed and sensitivity of a radio-frequency measurement and how to incorporate new tools, such as superconducting circuit elements and quantum-limited amplifiers into advanced radio-frequency experiments. Our aim is threefold: to introduce the readers to the technique, to review the advances to date, and to motivate new experiments in fast quantum device dynamics. Our intended audience includes experimentalists in the field of quantum electronics who want to implement radio-frequency experiments or improve them, together with physicists in related fields who want to understand how the most important radio-frequency measurements work.

Fast time-domain current measurement for quantum dot charge sensing using a homemade cryogenic transimpedance amplifier

We developed a high-speed and low-noise time-domain current measurement scheme using a homemade GaAs high-electron-mobility-transistor-based cryogenic transimpedance amplifier (TIA). The scheme is versatile for broad cryogenic current measurements, including semiconductor spin-qubit readout, owing to the TIA's having low input impedance comparable to that of commercial room-temperature TIAs. The TIA has a broad frequency bandwidth and a low noise floor, with a trade-off between them governed by the feedback resistance RFB. A lower RFB of 50 kΩ enables high-speed current measurement with a −3 dB cutoff frequency f−3dB = 28 MHz and noise-floor NF = 8.5 × 10−27 A2/Hz, while a larger RFB of 400 kΩ provides low-noise measurement with NF = 1.0 × 10−27 A2/Hz and f−3dB = 4.5 MHz. Time-domain measurement of a 2-nA peak-to-peak square wave, which mimics the output of the standard spin-qubit readout technique via charge sensing, demonstrates a signal-to-noise ratio (SNR) of 12.7, with the time resolution of 48 ns, for RFB = 200 kΩ, which compares favorably with the best-reported values for the radio frequency reflectometry technique. The time resolution can be further improved at the cost of the SNR (or vice versa) by using an even smaller (larger) RFB, with a further reduction in the noise figure possible by limiting the frequency band with a low-pass filter. Our scheme is best suited for readout electronics for cryogenic sensors that require a high time resolution and current sensitivity and, thus, provides a solution for various fundamental research and industrial applications.

Parametric exploration of zero-energy modes in three-terminal InSb-Al nanowire devices

We systematically study three-terminal InSb-Al nanowire devices by using radio-frequency reflectometry. Tunneling spectroscopy measurements on both ends of the hybrid nanowires are performed while systematically varying the chemical potential, magnetic field, and junction transparencies. Identifying the lowest-energy state allows for the construction of the lowest- and zero-energy state diagrams, which show how the states evolve as a function of the aforementioned parameters. Importantly, comparing the diagrams taken for each end of the hybrids enables the identification of states which do not coexist simultaneously, ruling out a significant amount of the parameter space as candidates for a topological phase. Furthermore, altering junction transparencies filters out zero-energy states sensitive to a local gate potential. Such a measurement strategy significantly reduces the time necessary to identify a potential topological phase and minimizes the risk of falsely recognizing trivial bound states as Majorana zero modes.

A Cryo-CMOS Wideband Quadrature Receiver With Frequency Synthesizer for Scalable Multiplexed Readout of Silicon Spin Qubits

In this article, a cryo-CMOS receiver integrated with a frequency synthesizer for scalable multiplexed readout of qubits is presented, focusing on radio frequency (RF) reflectometry readout of silicon-based semiconductor spin qubits/quantum dots. The proposed spin qubit readout chip consists of a wideband low noise amplifier (LNA), a quadrature mixer, a complex filter, a pair of in-phase/quadrature (I/Q) intermediate frequency (IF) amplifier chains, and a type-II charge-pump phase-locked loop (PLL) with a programmable frequency divider providing local oscillator (LO) signals. Noise optimizations are applied to the LNA design and the quadrature active mixer design to obtain the required performance. A mode-switching complementary voltage-controlled oscillator (VCO) is proposed to achieve low-power and low-phase noise in a wide-frequency tuning range (46.5%). Circuit modifications and design considerations for robust cryogenic temperature operation are presented and discussed. Measurements show that the receiver provides an average gain of 65 dB, a minimum noise figure of 0.5 dB, an IF bandwidth of 0.1–1.5 GHz, and an image rejection ratio of 23 dB at 3.5 K with a power consumption of 108 mW. This cryo-CMOS receiver with frequency synthesizer for spin qubit readout is a first step toward fully-integrated qubit readout and control.

Gate reflectometry of single-electron box arrays using calibrated low temperature matching networks

Sensitive dispersive readouts of single-electron devices (“gate reflectometry”) rely on one-port radio-frequency (RF) reflectometry to read out the state of the sensor. A standard practice in reflectometry measurements is to design an impedance transformer to match the impedance of the load to the characteristic impedance of the transmission line and thus obtain the best sensitivity and signal-to-noise ratio. This is particularly important for measuring large impedances, typical for dispersive readouts of single-electron devices because even a small mismatch will cause a strong signal degradation. When performing RF measurements, a calibration and error correction of the measurement apparatus must be performed in order to remove errors caused by unavoidable non-idealities of the measurement system. Lack of calibration makes optimizing a matching network difficult and ambiguous, and it also prevents a direct quantitative comparison between measurements taken of different devices or on different systems. We propose and demonstrate a simple straightforward method to design and optimize a pi matching network for readouts of devices with large impedance, Z ge 1hbox {M}Omega. It is based on a single low temperature calibrated measurement of an unadjusted network composed of a single L-section followed by a simple calculation to determine a value of the “balancing” capacitor needed to achieve matching conditions for a pi network. We demonstrate that the proposed calibration/error correction technique can be directly applied at low temperature using inexpensive calibration standards. Using proper modeling of the matching networks adjusted for low temperature operation the measurement system can be easily optimized to achieve the best conditions for energy transfer and targeted bandwidth, and can be used for quantitative measurements of the device impedance. In this work we use gate reflectometry to readout the signal generated by arrays of parallel-connected Al-AlOx single-electron boxes. Such arrays can be used as a fast nanoscale voltage sensor for scanning probe applications. We perform measurements of sensitivity and bandwidth for various settings of the matching network connected to arrays and obtain strong agreement with the simulations.

New progress of silicon-based semiconductor quantum computation

<sec>Spin qubits in silicon-based semiconductor quantum dots have become one of the prominent candidates for realizing fault-tolerant quantum computing due to their long coherence time, good controllability, and compatibility with modern advanced integrated circuit manufacturing processes. In recent years, due to the remarkable advances in silicon-based materials, the structure of quantum dot and its fabrication process, and qubit manipulation technology, the great progress of high-fidelity state preparation and readout, single- and two-qubit gates of spin qubits for silicon based semiconductor quantum computation has been achieved. The control fidelities for single- and two-qubit gates all exceed 99%—fault tolerance threshold required by the surface code known for its exceptionally high tolerance to errors. In this paper, we briefly introduce the basic concepts of silicon-based semiconductor quantum dots, discuss the state-of-art technologies used to improve the fidelities of single- and two-qubit gates, and finally highlight the research directions that should be focused on.</sec><sec>This paper is organized as follows. Firstly, we introduce three major types of quantum dot (QD) devices fabricated on different silicon-based substrates, including Si/SiGe heterojunction and Si/SiO<sub>2</sub>. The spin degree of electron or nucleus hosted in QD can be encoded into spin qubits. Electron spin qubits can be thermally initialized to ground state by using an electron reservoirs, and can be read out by spin-charge conversion mechanism: energy-selective readout (Elzerman readout) with reservoirs or Pauli spin blockade (PSB) without reservoirs. Additionally, high fidelity single-shot readout has been demonstrated by using radio-frequency gate reflectometry combined with the PSB, which has unique advantages in large-scale qubit array. To coherently control the spin qubits, electron dipole resonance (ESR) or electron dipole spin resonance (EDSR) for electron and nuclear magnetic resonance (NMR) for nucleus are introduced. With the help of isotope purification greatly improving the dephasing time of qubit and fast single-qubit manipulation based on EDSR, fidelity above 99.9% can be reached. For the two-qubit gates based on exchange interaction between electron spins, the strength of interaction <inline-formula><tex-math id="M1">\begin{document}$ J $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M1.png"/></alternatives></inline-formula> combined with Zeeman energy difference <inline-formula><tex-math id="M2">\begin{document}$ \Delta {E}_{z} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M2.png"/></alternatives></inline-formula> determines the energy levels of system, which lead to the different two-qubit gates, such as controlled-Z (CZ), controlled-Rotation (CROT), and the square root of the SWAP gate (<inline-formula><tex-math id="M3">\begin{document}$ \sqrt{\rm{S}\rm{W}\rm{A}\rm{P}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20221900_M3.png"/></alternatives></inline-formula>) gates. In order to improve the fidelity of two-qubit gates, a series of key technologies is used experimentally, they being isotope purification, symmetry operation, careful Hamiltonian engineering, and gate set tomography. Fidelity of two-qubit gates exceeding 99% has been demonstrated for electron spin qubits in Si/SiGe quantum dots and nuclear spin qubits in donors. These advances have pushed the silicon-based spin qubit platform to become a major stepping stone towards fault-tolerant quantum computation. Finally, we discuss the future study of spin qubits, that is, how to effectively expand the number of qubits, and many other problems to be explored and solved.</sec>

4.2\xa0K sensitivity-tunable radio frequency reflectometry of a physically defined p-channel silicon quantum dot

We demonstrate the measurement of p-channel silicon-on-insulator quantum dots at liquid helium temperatures by using a radio frequency (rf) reflectometry circuit comprising of two independently tunable GaAs varactors. This arrangement allows observing Coulomb diamonds at 4.2 K under nearly best matching condition and optimal signal-to-noise ratio. We also discuss the rf leakage induced by the presence of the large top gate in MOS nanostructures and its consequence on the efficiency of rf-reflectometry. These results open the way to fast and sensitive readout in multi-gate architectures, including multi qubit platforms.

Radio-frequency characterization of a supercurrent transistor made of a carbon nanotube

A supercurrent transistor is a superconductor–semiconductor hybrid device in which the Josephson supercurrent is switched on and off using a gate voltage. While such devices have been studied using DC transport, radio-frequency measurements allow for more sensitive and faster experiments. Here a supercurrent transistor made from a carbon nanotube is measured simultaneously via DC conductance and radio-frequency reflectometry. The radio-frequency measurement resolves all the main features of the conductance data across a wide range of bias and gate voltage, and many of these features are seen more clearly. These results are promising for measuring other kinds of hybrid superconducting devices, in particular for detecting the reactive component of the impedance, which a DC measurement can never detect.

Radio-Frequency Reflectometry in Silicon-Based Quantum Dots

Radio-frequency (rf) reflectometry offers a fast and sensitive method for charge sensing and spin readout in gated quantum dots. We focus in this work on the implementation of rf readout in accumulation-mode gate-defined quantum dots, where the large parasitic capacitance poses a challenge. We describe and test two methods for mitigating the effect of the parasitic capacitance, one by on-chip modifications and a second by off-chip changes. We demonstrate that on-chip modifications enable high-performance charge readout in $\mathrm{Si}$/${\mathrm{Si}}_{x}$${\mathrm{Ge}}_{1\ensuremath{-}x}$ quantum dots, achieving a fidelity of 99.9% for a measurement time of $1\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$.

Novel characterization of dopant-based qubits

Silicon is a leading qubit platform thanks to the exceptional coherence times that can be achieved and to the available commercial manufacturing platform for integration. Building scalable quantum processing architectures relies on accurate quantum state manipulation, which can only be achieved through a complete understanding of the underlying quantum state properties. This article reviews the electrical methods that have been developed to probe the quantum states encoded in individual and interacting atom qubits in silicon, from the pioneering single electron tunneling spectroscopy framework in nanoscale transistors, to radio frequency reflectometry to probe coherence properties and scanning tunneling microscopy to directly image the wave function at the atomic scale. Together with the development of atomistic simulations of realistic devices, these methods are today applied to other emerging dopant and optically addressable defect states to accelerate the engineering of quantum technologies in silicon.