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arXiv:2209.15086 · Physical Review Applied

Intrinsic noise of the single-electron box

Laurence Cochrane, Ashwin A. Seshia, M. Fernando González-Zalba

Published Jun 28, 2024• 5 citations
arXivHTMLPDF

Abstract

The radio-frequency (rf) single-electron box is becoming an attractive charge sensor for semiconductor-based quantum computing devices due to its high sensitivity and small footprint, which facilitate the design of highly connected qubit architectures. However, an understanding of its ultimate sensitivity is missing due to the lack of a noise model. Here, we quantify the intrinsic noise of the single-electron box arising from stochastic cyclic electron tunneling between a quantum dot and a reservoir driven by a periodic gate voltage. We use both a master-equation formalism and Markov Monte Carlo simulations to calculate the gate-noise current and find that the noise mechanism can be represented as a cyclostationary process. We consider the implications of this cyclostationary noise on the ultimate sensitivity of single-electron box sensors for fast high-fidelity readout of spin qubits, in particular evaluating results for rf reflectometry implementations and the back action of the sensor on a qubit. Furthermore, we determine the conditions under which the intrinsic noise limit could be measured experimentally and techniques by which the noise can be suppressed to enhance qubit-readout fidelity. Published by the American Physical Society 2024

DOI
10.1103/physrevapplied.21.064066

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The radio-frequency (rf) single-electron box is becoming an attractive charge sensor for semiconductor-based quantum computing devices due to its high sensitivity and small footprint, which facilitate the design of highly connected qubit architectures. However, an understanding of its ultimate sensitivity is missing due to the lack of a noise model. Here, we quantify the intrinsic noise of the single-electron box arising from stochastic cyclic electron tunneling between a quantum dot and a reservoir driven by a periodic gate voltage. We use both a master-equation formalism and Markov Monte Carlo simulations to calculate the gate-noise current and find that the noise mechanism can be represented as a cyclostationary process. We consider the implications of this cyclostationary noise on the ultimate sensitivity of single-electron box sensors for fast high-fidelity readout of spin qubits, in particular evaluating results for rf reflectometry implementations and the back action of the sensor on a qubit. Furthermore, we determine the conditions under which the intrinsic noise limit could be measured experimentally and techniques by which the noise can be suppressed to enhance qubit-readout fidelity. Published by the American Physical Society 2024
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The radio-frequency superconducting single electron transistor (RF-SET) is a highly sensitive and fast electrometer operating near the quantum limit. The back-action current noise of the SET induces voltage fluctuations on the system it is coupled to, dephasing its charge states. Here we propose to study the back action of the RF-SET by means of a double quantum dot (DQD) and, an RF-SET electrostatically coupled to one of the two dots. The inelastic current through the DQD is very sensitive to the spectral density of the voltage fluctuations in the nearby environment. By properly choosing the dot size and inter-dot tunnel barrier thickness, one can cause inelastic process to dominate the transport processes. A measurement of the inelastic current through the double dot system can then be used to calculate the spectral density of noise associated with the RF-SET and hence its back action. The design, fabrication and characterization of an RF-SET/DQD system is discussed in this work. Real-time studies of electron dynamics in coupled dots are also addressed.
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Electron cotunneling in semiconductor quantum dots is a higher-order tunneling mechanism that connects initial and final charge states through energetically inaccessible virtual intermediate configurations. In quantum-dot arrays, such processes can produce simultaneous charge motion across multiple tunnel junctions and enable transitions that would otherwise be suppressed by Coulomb blockade. Here, building on an earlier proof-of-principle demonstration, we investigate radio-frequency (rf)-driven correlated cotunneling and its application to dispersive quantum-dot readout. Using both theoretical modeling and experimental measurements in two different foundry-fabricated silicon devices, we show that an external rf drive can induce correlated cyclic single-electron transitions, resulting in enhanced charge-polarization of the system. We develop a general theoretical framework for rf electron-cascade readout, which exploits cotunneling events in quantum-dot systems with three or more dots to produce a relative signal enhancement, and extend its experimental demonstration to a gate-sensed device architecture. Our results establish the operating principles of rf electron-cascade readout and provide a route to increased dispersive readout fidelity in semiconductor quantum computing architectures.
High-fidelity qubit readout is critical in order to obtain the thresholds needed to implement quantum error-correction protocols and achieve fault-tolerant quantum computing. Large-scale silicon qubit devices will have densely packed arrays of quantum dots with multiple charge sensors that are, on average, farther away from the quantum dots, entailing a reduction in readout fidelities. Here, we present a readout technique that enhances the readout fidelity in a linear SiMOS four-dot array by amplifying correlations between a pair of single-electron transistors, known as a twin SET. By recording and subsequently correlating the twin SET traces as we modulate the dot detuning across a charge transition, we demonstrate a reduction in the charge readout infidelity by over one order of magnitude compared to traditional readout methods. We also study the spin-to-charge conversion errors introduced by the modulation technique and conclude that faster modulation frequencies avoid relaxation-induced errors without introducing significant spin-flip errors, favoring the use of the technique at short integration times. This method not only allows for faster and higher-fidelity qubit measurements but it also enhances the signal corresponding to charge transitions that take place farther away from the sensors, enabling a way to circumvent the reduction in readout fidelities in large arrays of qubits. Published by the American Physical Society 2024
Charge detection at microsecond time-scales has far reaching consequences in both technology and in our understanding of electron dynamics in nanoscale devices such as quantum dots. Radio-frequency superconducting single electron transistors (RF-SET) and quantum point contacts (QPC) are ultra sensitive charge sensors operating near the quantum limit. The operation of RF-SETs outside the superconducting gap has been a topic of study; the sub-gap operation, especially in the presence of large quantum fluctuations of quasiparticles remains largely unexplored, both theoretically and experimentally. We have investigated the effects of quantum fluctuations of quasiparticles on the operation of RF-SETs for large values of the quasiparticle cotunneling parameter alpha = 8EJ/Ec, where EJ and Ec are the Josephson and charging energies. We find that, for alpha > 1, sub-gap RF-SET operation is still feasible despite quantum fluctuations that wash out quasiparticle tunneling thresholds. Such RF-SETs show linearity and signal-to-noise ratio superior to those obtained when quantum fluctuations are weak, while still demonstrating excellent charge sensitivity.\nWe have operated a QPC charge detector in a radio frequency mode that allows fast charge detection in a bandwidth of several megahertz. The noise limiting the sensitivity of the charge detector is not the noise of a secondary amplifier, but the non-equilibrium device noise of the QPC itself. The noise power averaged over a measurement bandwidth of about 10MHz around the carrier frequency is in agreement with the theory of photon-assisted shot noise. Frequency-resolved measurements, however show several significant discrepancies with the theoretical predictions. The measurement techniques developed can also be used to investigate the noise of other semiconductor nanostructures such as quantum dots in the Kondo regime.\nA study of the noise characteristics alone can not determine whether the device is operating at the quantum limit; a characterization of back action is also necessary. The inelastic current through a double quantum dot system (DQD) is sensitive to the spectral density of voltage fluctuations in its electromagnetic environment. Electrical transport studies on a DQD system electrostatically coupled to an SET shows qualitative evidence of back-action of SET. The design and fabrication of a few electron DQD device with integrated RF-SET and QPC charge sensors for the study of back action of the sensors and real-time electron dynamics in the DQD are also discussed.