Radio-frequency Single-electron Transistor Research Articles

Radio-frequency single electron transistors in physically defined silicon quantum dots with a sensitive phase response

Radio-frequency reflectometry techniques are instrumental for spin qubit readout in semiconductor quantum dots. However, a large phase response is difficult to achieve in practice. In this work, we report radio-frequency single electron transistors using physically defined quantum dots in silicon-on-insulator. We study quantum dots which do not have the top gate structure considered to hinder radio frequency reflectometry measurements using physically defined quantum dots. Based on the model which properly takes into account the parasitic components, we precisely determine the gate-dependent device admittance. Clear Coulomb peaks are observed in the amplitude and the phase of the reflection coefficient, with a remarkably large phase signal of ∼45°. Electrical circuit analysis indicates that it can be attributed to a good impedance matching and a detuning from the resonance frequency. We anticipate that our results will be useful in designing and simulating reflectometry circuits to optimize qubit readout sensitivity and speed.

Radio-Frequency Capacitive Gate-Based Sensing

Developing fast, accurate and scalable techniques for quantum state readout is an active area in semiconductor-based quantum computing. Here, we present results on dispersive sensing of silicon corner state quantum dots coupled to lumped-element electrical resonators via the gate. The gate capacitance of the quantum device is configured in parallel with a superconducting spiral inductor resulting in resonators with loaded Q-factors in the 400-800 range. For a resonator operating at 330 MHz, we achieve a charge sensitivity of 7.7 $\mu$e$/\sqrt{\text{Hz}}$ and, when operating at 616 MHz, we get 1.3 $\mu$e$/\sqrt{\text{Hz}}$. We perform a parametric study of the resonator to reveal its optimal operation points and perform a circuit analysis to determine the best resonator design. The results place gate-based sensing at par with the best reported radio-frequency single-electron transistor sensitivities while providing a fast and compact method for quantum state readout.

High-Precision Displacement Sensing of Monolithic Piezoelectric Disk Resonators Using a Single-Electron Transistor

A single-electron transistor (SET) can be used as an extremely sensitive charge detector. Mechanical displacements can be converted into charge, and hence, SETs can become sensitive detectors of mechanical oscillations. For studying small-energy oscillations, an important approach to realize the mechanical resonators is to use piezoelectric materials. Besides coupling to traditional electric circuitry, the strain-generated piezoelectric charge allows for measuring ultrasmall oscillations via SET detection. Here, we explore the usage of SETs to detect the shear-mode oscillations of a 6-mm-diameter quartz disk resonator with a resonance frequency around 9 MHz. We measure the mechanical oscillations using either a conventional DC SET, or use the SET as a homodyne or heterodyne mixer, or finally, as a radio-frequency single-electron transistor (RF-SET). The RF-SET readout is shown to be the most sensitive method, allowing us to measure mechanical displacement amplitudes below 1E-13 m. We conclude that a detection based on a SET offers a potential to reach the sensitivity at the quantum limit of the mechanical vibrations.

Tunneling Statistics for Analysis of Spin-Readout Fidelity

We investigate spin and charge dynamics of a quantum dot of phosphorus atoms coupled to a radio-frequency single-electron transistor (rf-SET) using full counting statistics. We show how the magnetic field plays a role in determining the bunching or anti-bunching tunnelling statistics of the donor dot and SET system. Using the counting statistics we show how to determine the lowest magnetic field where spin-readout is possible. We then show how such a measurement can be used to investigate and optimise single electron spin-readout fidelity.

Modeling a radio-frequency single-electron-transistor scanning probe

Single-electron transistors (SETs) are ultra-sensitive charge sensors. Aiming to develop a radio-frequency single-electron-transistor (RF-SET) scanning probe system, we build a complete device/circuit model to evaluate the charge sensitivity and the spatial resolution. Simulations of a gedunken experiment in which a silicon RF-SET probe scans a nanowire device suggest a charge sensitivity in the order of 10−5–10−3 e/Hz1/2 and a spatial resolution better than 100 nm. The dynamic range and the linearity of the scanning probe are also discussed. The model would provide a quantitative interpretation for future real imaging experiment and an operation guidance for a realistic RF-SET scanning probe system.

Overall performance evaluation using an equivalent circuit model for radio-frequency single-electron transistors

Charge sensitivities of a radio-frequency single-electron transistor (RF-SET) by using amplitude (AD) and phase-shift detection (PSD) of the reflected RF signals were experimentally studied. It was found that AD is most sensitive at the resonant frequency while PSD is most sensitive at a frequency slightly off the resonance. The best PSD sensitivity is better than the best AD one when the quality factor of a tank circuit is higher than 10; the higher Q-value is, the superior PSD. The maximal change in reflection amplitude and phase-shift were found proportional to the SET conductance change. The above experimental findings were confirmed by the calculation based on an equivalent circuit model.

Proposal for a Loophole-Free Bell Test with Electron Spins of Donors in Silicon

So far, all experimental tests of Bell inequalities which must be satisfied by all local realistic hidden-variable theories and are violated by quantum mechanical predictions have left at least one loophole open. We propose a feasible setup allowing for a loophole-free test of the Bell inequalities. Two electron spin qubits of donors31P in a nanoscale silicon host in different cavities 300 m apart are entangled through a bright coherent light and postselections using homodyne measurements. The electron spins are then read out randomly and independently by Alice and Bob, respectively, with unity efficiency in less than 0.7 µs by using optically induced spin to charge transduction detected by radio-frequency single electron transistor. A violation of Bell inequality larger than 37% and 18% is achievable provided that the detection accuracy is 0.99 and 0.95, respectively.

Rf-electrometer using a carbon nanotube resonant tunneling transistor

We have studied resonant tunneling transistors (RTT) made of single-walled carbon nanotube quantum dots in the Fabry–Pérot regime. We show sensitivity to input charge as high as 5×10−6 e/Hz1/2 with a carrier frequency of 719 MHz at 4.2 K. This result is comparable to the best values of charge sensitivity so far reported for radio frequency single electron transistors (rf-SET). Unlike SETs, whose operating temperature is limited as Coulomb blockade vanishes as 1/T, a RTT can operate at higher temperatures, since the dephasing length lϕ∝1/T2/3.

Radio frequency operation of clocked quantum-dot cellular automata latch

The radio frequency operation of a single-electron latch based on Al–AlOx–Al tunnel junctions is presented. By capacitively coupling the latch to a radio frequency single electron transistor, charge switching on the microsecond timescale is demonstrated. The fast switching and high repeatability of the latch response indicates that high speed operation of pipelines, signal fan-outs, and more complex logic devices are possible with this technology. The experimental technique developed is also promising for enabling the investigation of the intrinsic switching speed in electronic quantum-dot cellular automata-based circuits.

Cryogenic instrumentation for fast current measurement in a silicon single electron transistor

We present a realization of high bandwidth instrumentation at cryogenic temperatures and for dilution refrigerator operation that possesses advantages over methods using radio frequency single electron transistor or transimpedance amplifiers. The ability for the low temperature electronics to carry out faster measurements than with room temperature electronics is investigated by the use of a phosphorous-doped single electron transistor. A single shot technique is successfully implemented and used to observe the real-time decay of a quantum state. A discussion on various measurement strategies is presented and the consequences on electron heating and noise are analyzed.

Progress in the development of a single Cooper-pair box qubit

We describe in this review progress in techniques for measuring the quantum states of the single Cooper-pair box (SCB) at the Jet Propulsion Laboratory, and the use of these techniques to characterize their performance as quantum bits. Initially, the Radio-Frequency-Single-Electron Transistor was used to measure conventional and differential versions of the SCB. To overcome some of the difficulties associated with the radio-frequency single-electron transistor, a transition was made to readout based on the quantum capacitance technique. Using this method, entanglement between two SCBs was demonstrated spectroscopically and with ground state characterization.

Simulation method for transmission-type radio-frequency single-electron transistor (RF-SET) operation by SPICE

An efficient simulation method for transmission-type radio-frequency single-electron transistors (RF-SETs) is developed. By introducing equivalent circuits of propagating microwaves through RF cables, we solve the master equation for RF-SETs self-consistently by using the conventional circuit simulator SPICE together with the SET current model. By examining transmitted waves from the transmission-type RF-SET, we show that the developed method successfully reproduces the numerical reference methods (calculated self- consistently). We also show that our method provides simple and fast ways to simulate and analyze RF-SETs even under complicated circuit geometry and in high frequencies over GHz. Based on the developed simulation method, we introduce the modulation technique to estimate the charge sensitivity of the transmission-type RF-SET.

Silicon-on-Insulator-Based Radio Frequency Single-Electron Transistors Operating at Temperatures above 4.2 K

A radio frequency single-electron transistor (RF-SET) based on a silicon-on-insulator (SOI) substrate is demonstrated to operate successfully at temperatures above 4.2 K. The SOI SET was fabricated by inducing lateral constrictions in doped SOI nanowires. The device structure was optimized to overcome the inherent drawback of high resistance with the SOI SETs. We performed temperature variation measurements after five thermal cyclings of the same sample to 4.2 K and found that the single-dot device transport characteristics are highly stable. The charge sensitivity was measured to be 36 microe(rms) Hz(-1/2) at 4.2 K, and the RF-SET operation was demonstrated up to 12.5 K for the first time. This work is an important prerequisite to realizing operation of RF-SETs at noncryogenic temperatures.

Highly sensitive and broadband carbon nanotube radio-frequency single-electron transistor

We have investigated radio-frequency single-electron transistor operation of single-walled carbon nanotube quantum dots in the strong tunneling regime. At a temperature of 4.2 K and with a carrier frequency of 754.2 MHz, we reach a charge sensitivity of 2.3×10−6e/Hz over a bandwidth of 85 MHz. Our results indicate a gain-bandwidth product of 3.7×1013 Hz(3/2)/e, which is by one order of magnitude better than those for typical radio-frequency single-electron transistors.

Proposal for a loophole-free test of nonlocal realism with electron spins of donors

The deep-rooted concept of ``realism''---a viewpoint according to which an external reality exists independent of observation, may have been shaken to some extent by a recent surprising advance in experimental test of a broad class of nonlocal hidden-variable (NLHV) theories [S. Gr\"oblacher, T. Paterek, R. Kaltenbaek, \ifmmode \check{C}\else \v{C}\fi{}. Brukner, M. \ifmmode \dot{Z}\else \.{Z}\fi{}ukowski, M. Aspelmeyer, and A. Zeilinger, Nature (London) 446, 871 (2007)], though there exists a detection loophole. In this paper a feasible propose for a loophole-free test of non-local realism is discussed based on the independent readout of two electron spins of donors $^{31}\text{P}$ in semiconductors in different cavities entangled through a 4.4 dB bright squeezed coherent light and a postselection based on homodyne measurement. The electron spins are read out by using optically induced spin to charge transduction detected by radio-frequency single electron transistor.

Impact of Key Circuit Parameters on Signal-to-Noise Ratio Characteristics for the Radio Frequency Single-Electron Transistors

Hybrid simulation was performed to analyze the response of the real-time reflection-type radio frequency single-electron transistor (RF-SET) measurement system. A compact and physically-based analytical SET model, which was validated with a Monte Carlo simulator, was used to simulate the SET characteristics, while SPICE equivalent circuits were implemented to simulate all other components of the RF-SET measurement system. The impact of various key parameters on the RF-SET response was demonstrated for a carrier frequency much less than I/e ( is the typical current through the SET). It was revealed that an inevitable feed-through loss between the tank circuit and the cryogenic amplifier, and high-frequency parasitics of the inductor degrade the RF-SET performance significantly. As such, they have to be optimized to experimentally realize the shot-noise-limited charge sensitivity.

A silicon radio-frequency single electron transistor

We report the demonstration of a silicon radio-frequency single electron transistor. The island is defined by electrostatically tunable tunnel barriers in a narrow channel field effect transistor. Charge sensitivities of better than 10μe∕Hz are demonstrated at megahertz bandwidth. These results demonstrate that silicon may be used to fabricate fast, sensitive electrometers.

A Radio Frequency Single-Electron Transistor Based on an InAs/InP Heterostructure Nanowire

We demonstrate radio frequency single-electron transistors fabricated from epitaxially grown InAs/InP heterostructure nanowires. Two sets of double-barrier wires with different barrier thicknesses were grown. The wires were suspended 15 nm above a metal gate electrode. Electrical measurements on a high-resistance nanowire showed regularly spaced Coulomb oscillations at a gate voltage from -0.5 to at least 1.8 V. The charge sensitivity was measured to 32 microe rms Hz(-1/2) at 1.5 K. A low-resistance single-electron transistor showed regularly spaced oscillations only in a small gate-voltage region just before carrier depletion. This device had a charge sensitivity of 2.5 microe rms Hz(-1/2). At low frequencies this device showed a typical 1/f noise behavior, with a level extrapolated to 300 microe rms Hz(-1/2) at 10 Hz.

Transport Characteristics of Mesoscopic Radio-Frequency Single Electron Transistor

The transport property of a quantum dot under the influence of external time-dependent field is investigated. The mesoscopic device is modelled as semiconductor quantum dot coupled weakly to superconducting leads via asymmetric double tunnel barriers of different heights. An expression for the current is deduced by using the Landauer–Buttiker formula, taking into consideration of both the Coulomb blockade effect and the magnetic field. It is found that the periodic oscillation of the current with the magnetic field is controlled by the ratio of the frequency of the applied ac-field to the electron cyclotron frequency. Our results show that the present device operates as a radio-frequency single electron transistor.

Operation of single-walled carbon nanotube as a radio-frequency single-electrontransistor

We demonstrate the operation of a radio-frequency single-electron transistor (RF-SET) usingsingle-wall carbon nanotubes (SWNTs). The device is embedded in a resonant tank circuit andoperates in reflection mode at temperatures as high as 5 K. Both frequency domain and timedomain results are presented. With a gate modulation frequency of 1 MHz, a charge sensitivity of∼4.78 × 10−4e/Hz−1/2 is obtained, which is limited by the large parasitic capacitance between the gate and thesource/drain pads. Through the use of a top-gated configuration with reduced parasiticcapacitance, both the RF performance and the charge sensitivity can be significantlyimproved.