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The ability for optically active media to rotate the polarization of light is the basis of polarimetry, an illustrious technique responsible for many breakthroughs in fields as varied as astronomy, medicine and material science. Here, we recast the primary mechanism for spin readout in semiconductor-based quantum computers, Pauli spin-blockade (PSB), as the natural extension of polarimetry to the third dimension. We perform polarimetry with spins through a silicon quantum dot exchanging a hole with a boron acceptor, demonstrating the role of spin-orbit coupling in creating spin misalignment. Perfect spin alignment may be recovered by means of rotating the applied magnetic-field orientation. This work shows how spin misalignment sets a fundamental upper limit for the spin readout fidelity in quantum-computing systems based on PSB.

A quantum system interacting with a time-periodic excitation creates a ladder of hybrid eigenstates in which the system is mixed with an increasing number of photons. This mechanism, referred to as dressing, has been observed in the context of light-matter interaction in systems as varied as atoms, molecules and solid-state qubits. In this work, we demonstrate state dressing in a semiconductor quantum dot tunnel-coupled to a charge reservoir. We observe the emergence of a Floquet ladder of states in the system's high-frequency electrical response, manifesting as interference fringes at the multiphoton resonances despite the system lacking an avoided crossing. We study the dressed quantum dot while changing reservoir temperature, charge lifetime, and excitation amplitude and reveal the fundamental nature of the mechanism by developing a theory based on the quantum dynamics of the Floquet ladder, which is in excellent agreement with the data. Furthermore, we show how the technique finds applications in the accurate electrostatic characterisation of semiconductor quantum dots., Comment: 8 Pages, 4 Figures. Supplementary: 4 Pages, 2 Figures

In semiconductor nanostructures, spin blockade (SB) is the most scalable mechanism for electrical spin readout requiring only two bound spins for its implementation which, in conjunction with charge sensing techniques, has led to high-fidelity readout of spins in semiconductor-based quantum processors. However, various mechanisms may lift SB, such as strong spin-orbit coupling (SOC) or low-lying excited states, hence posing challenges to perform spin readout at scale and with high fidelity in such systems. Here, we present a method, based on the dependence of the two-spin system polarizability on energy detuning, to perform spin state readout even when SB lifting mechanisms are dominant. It leverages SB lifting as a resource to detect different spin measurement outcomes selectively and positively. We demonstrate the method using a hybrid system formed by a quantum dot (QD) and a Boron acceptor in a silicon p-type transistor and show spin selective and positive readout of different spin states under SB lifting conditions due to (i) SOC and (ii) low-lying orbital states in the QD. We further use the method to determine the detuning-dependent spin relaxation time of 0.1-8~$\mu$s. Our method should help perform high-fidelity projective spin measurements in systems subject to strong SOC and may facilitate quantum tomography and state leakage studies., Comment: 13 pages, 10 figures

Fast measurements of quantum devices is important in areas such as quantum sensing, quantum computing and nanodevice quality analysis. Here, we develop a superconductor-semiconductor multi-module microwave assembly to demonstrate charge state readout at the state-of-the-art. The assembly consist of a superconducting readout resonator interfaced to a silicon-on-insulator (SOI) chiplet containing quantum dots (QDs) in a high-$\kappa$ nanowire transistor. The superconducting chiplet contains resonant and coupling elements as well as $LC$ filters that, when interfaced with the silicon chip, result in a resonant frequency $f=2.12$ GHz, a loaded quality factor $Q=850$, and a resonator impedance $Z=470$ $\Omega$. Combined with the large gate lever arms of SOI technology, we achieve a minimum integration time for single and double QD transitions of 2.77 ns and 13.5 ns, respectively. We utilize the assembly to measure charge noise over 9 decades of frequency up to 500 kHz and find a 1/$f$ dependence across the whole frequency spectrum as well as a charge noise level of 4 $\mu$eV/$\sqrt{\text{Hz}}$ at 1 Hz. The modular microwave circuitry presented here can be directly utilized in conjunction with other quantum device to improve the readout performance as well as enable large bandwidth noise spectroscopy, all without the complexity of superconductor-semiconductor monolithic fabrication., Comment: Main: 8 pages, 4 figures. Supplementary: 4 pages, 7 figures

We report fast charge state readout of a double quantum dot in a CMOS split-gate silicon nanowire transistor via the large dispersive interaction with microwave photons in a lumped-element resonator formed by hybrid integration with a superconducting inductor. We achieve a coupling rate $g_0/(2\pi) = 204 \pm 2$ MHz by exploiting the large interdot gate lever arm of an asymmetric split-gate device, $\alpha=0.72$, and by inductively coupling to the resonator to increase its impedance, $Z_\text{r}=560~\Omega$. In the dispersive regime, the large coupling strength at the double quantum dot hybridisation point produces a frequency shift comparable to the resonator linewidth, the optimal setting for maximum state visibility. We exploit this regime to demonstrate rapid dispersive readout of the charge degree of freedom, with a SNR of 3.3 in 50 ns. In the resonant regime, the fast charge decoherence rate precludes reaching the strong coupling regime, but we show a clear route to spin-photon circuit quantum electrodynamics using hybrid CMOS systems., Comment: Accepted manuscript

We fabricated Quantum Dot (QD) devices using a standard SOI CMOS process flow, and demonstrated that the spin of confined electrons could be controlled via a local electrical-field excitation, owing to inter-valley spin-orbit coupling. We discuss that modulating the confinement geometry via an additional electrode may enable switching a quantum bit (qubit) between an electrically-addressable valley configuration and a protected spin configuration. This proposed scheme bears relevance to improve the trade-off between fast operations and slow decoherence for quantum computing on a Si qubit platform. Finally, we evoke the impact of process-induced variability on the operating bias range., Comment: arXiv admin note: substantial text overlap with arXiv:1912.09806

The implementation of quantum technologies in electronics leads naturally to the concept of coherent single-electron circuits, in which a single charge is used coherently to provide enhanced performance. In this work, we propose a coherent single-electron device that operates as an electrically-tunable capacitor. This system exhibits a sinusoidal dependence of the capacitance with voltage, in which the amplitude of the capacitance changes and the voltage period can be tuned by electric means. The device concept is based on double-passage Landau-Zener-St\"uckelberg-Majorana interferometry of a coupled two-level system that is further tunnel-coupled to an electron reservoir. We test this model experimentally by performing Landau-Zener-St\"uckelberg-Majorana interferometry in a single-electron double quantum dot coupled to an electron reservoir and show that the voltage period of the capacitance oscillations is directly proportional to the excitation frequency and that the amplitude of the oscillations depends on the dynamical parameters of the system: intrinsic relaxation and coherence time, as well as the tunneling rate to the reservoir. Our work opens up an opportunity to use the non-linear capacitance of double quantum dots to obtain enhanced device functionalities.

The engineering of electron spin qubits in a compact unit cell embedding all quantum functionalities is mandatory for large scale integration. In particular, the development of a high-fidelity and scalable spin readout method remains an open challenge. Here we demonstrate high-fidelity and robust spin readout based on gate reflectometry in a CMOS device comprising one qubit dot and one ancillary dot coupled to an electron reservoir to perform readout. This scalable method allows us to read out a spin with a fidelity above 99% for 1 ms integration time. To achieve such fidelity, we exploit a latched spin blockade mechanism that requires electron exchange between the ancillary dot and the reservoir. We show that the demonstrated high read-out fidelity is fully preserved up to 0.5 K. This results holds particular relevance for the future co-integration of spin qubits and classical control electronics., Comment: 6 pages, 4 figures

We present a sensitive, tunable radio-frequency resonator designed to detect reactive changes in nanoelectronic devices down to dilution refrigerator temperatures. The resonator incorporates GaAs varicap diodes to allow electrical tuning of the resonant frequency and the coupling to the input line. We find a resonant frequency tuning range of 8.4 MHz at 55 mK that increases to 29 MHz at 1.5 K. To assess the impact on performance of different tuning conditions, we connect a quantum dot in a silicon nanowire field-effect transistor to the resonator, and measure changes in the device capacitance caused by cyclic electron tunneling. At 250 mK, we obtain an equivalent charge sensitivity of $43~\mu e / \sqrt{\text{Hz}}$ when the resonator and the line are impedance-matched and show that this sensitivity can be further improved to $31~\mu e / \sqrt{\text{Hz}}$ by re-tuning the resonator. We understand this improvement by using an equivalent circuit model and demonstrate that for maximum sensitivity to capacitance changes, in addition to impedance matching, a high-quality resonator with low parasitic capacitance is desired., Comment: Includes supplementary information

Quantum shot noise probes the dynamics of charge transfers through a quantum conductor, reflecting whether quasiparticles flow across the conductor in a steady stream, or in syncopated bursts. We have performed high-sensitivity shot noise measurements in a quantum dot obtained in a silicon metal-oxide-semiconductor field-effect transistor. The quality of our device allows us to precisely associate the different transport regimes and their statistics with the internal state of the quantum dot. In particular, we report on large current fluctuations in the inelastic cotunneling regime, corresponding to different highly-correlated, non-Markovian charge transfer processes. We have also observed unusually large current fluctuations at low energy in the elastic cotunneling regime, the origin of which remains to be fully investigated., Comment: Includes supplementary material

We perform an excited state spectroscopy analysis of a silicon corner dot in a nanowire field-effect transistor to assess the electric field tunability of the valley splitting. First, we demonstrate a back-gate-controlled transition between a single quantum dot and a double quantum dot in parallel that allows tuning the device in to corner dot formation. We find a linear dependence of the valley splitting on back-gate voltage, from $880~\mu \text{eV}$ to $610~\mu \text{eV}$ with a slope of $-45\pm 3~\mu \text{eV/V}$ (or equivalently a slope of $-48\pm 3~\mu \text{eV/(MV/m)}$ with respect to the effective field). The experimental results are backed up by tight-binding simulations that include the effect of surface roughness, remote charges in the gate stack and discrete dopants in the channel. Our results demonstrate a way to electrically tune the valley splitting in silicon-on-insulator-based quantum dots, a requirement to achieve all-electrical manipulation of silicon spin qubits., Comment: 5 pages, 3 figures. In this version: Discussion of model expanded; Fig. 3 updated; Refs. added (15, 22, 32, 34, 35, 36, 37)

Temperature is a fundamental parameter in the study of physical phenomena. At the nanoscale, local temperature differences can be harnessed to design novel thermal nanoelectronic devices or test quantum thermodynamical concepts. Determining temperature locally is hence of particular relevance. Here, we present a primary electron thermometer that allows probing the local temperature of a single electron reservoir in single-electron devices. The thermometer is based on cyclic electron tunneling between a system with discrete energy levels and a single electron reservoir. When driven at a finite rate, close to a charge degeneracy point, the system behaves like a variable capacitor whose magnitude and line-shape varies with temperature. In this experiment, we demonstrate this type of thermometer using a quantum dot in a CMOS nanowire transistor. We drive cyclic electron tunneling by embedding the device in a radio-frequency resonator which in turn allows us to read the thermometer dispersively. We find that the full width at half maximum of the resonator phase response depends linearly with temperature via well known physical law by using the ratio $k_\text{B}/e$ between the Boltzmann constant and the electron charge. Overall, the thermometer shows potential for local probing of fast heat dynamics in nanoelectronic devices and for seamless integration with silicon-based quantum circuits.

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.

In a semiconductor spin qubit with sizable spin-orbit coupling, coherent spin rotations can be driven by a resonant gate-voltage modulation. Recently, we have exploited this opportunity in the experimental demonstration of a hole spin qubit in a silicon device. Here we investigate the underlying physical mechanisms by measuring the full angular dependence of the Rabi frequency as well as the gate-voltage dependence and anisotropy of the hole $g$-factors. We show that a $g$-matrix formalism can simultaneously capture and discriminate the contributions of two mechanisms so far independently discussed in the literature: one associated with the modulation of the $g$ factors, and measurable by Zeeman energy spectroscopy, the other not. Our approach has a general validity and can be applied to the analysis of other types of spin-orbit qubits., Comment: Letter format (4 pages, 4 figures). Detailed theory in Supplemenatl Material

We study Landau-Zener-Stueckelberg-Majorana (LZSM) interferometry under the influence of projective readout using a charge qubit tunnel-coupled to a fermionic sea. This allows us to characterise the coherent charge qubit dynamics in the strong-driving regime. The device is realised within a silicon complementary metal-oxide-semiconductor (CMOS) transistor. We first read out the charge state of the system in a continuous non-demolition manner by measuring the dispersive response of a high-frequency electrical resonator coupled to the quantum system via the gate. By performing multiple fast passages around the qubit avoided crossing, we observe a multi-passage LZSM interferometry pattern. At larger driving amplitudes, a projective measurement to an even-parity charge state is realised, showing a strong enhancement of the dispersive readout signal. At even larger driving amplitudes, two projective measurements are realised within the coherent evolution resulting in the disappearance of the interference pattern. Our results demonstrate a way to increase the state readout signal of coherent quantum systems and replicate single-electron analogues of optical interferometry within a CMOS transistor.

The ability to manipulate electron spins with voltage-dependent electric fields is key to the operation of quantum spintronics devices, such as spin-based semiconductor qubits. A natural approach to electrical spin control exploits the spin-orbit coupling (SOC) inherently present in all materials. So far, this approach could not be applied to electrons in silicon, due to their extremely weak SOC. Here we report an experimental realization of electrically driven electron-spin resonance in a silicon-on-insulator (SOI) nanowire quantum dot device. The underlying driving mechanism results from an interplay between SOC and the multi-valley structure of the silicon conduction band, which is enhanced in the investigated nanowire geometry. We present a simple model capturing the essential physics and use tight-binding simulations for a more quantitative analysis. We discuss the relevance of our findings to the development of compact and scalable electron-spin qubits in silicon.

We report on hole compact double quantum dots fabricated using conventional CMOS technology. We provide evidence of Pauli spin blockade in the few hole regime which is relevant to spin qubit implementations. A current dip is observed around zero magnetic field, in agreement with the expected behavior for the case of strong spin-orbit. We deduce an intradot spin relaxation rate $\approx$120\,kHz for the first holes, an important step towards a robust hole spin-orbit qubit.

We investigate a hybrid metallic island / single dopant electron pump based on fully-depleted silicon on insulator technology. Electron transfer between the central metallic island and the leads is controlled by resonant tunneling through single phosphorus dopants in the barriers. Top gates above the barriers are used control the resonance conditions. Applying radio frequency signals to the gates, non-adiabatic quantized electron pumping is achieved. A simple deterministic model is presented and confirmed by comparing measurements with simulations.

We compute the contact resistances $R_{\rm c}$ in trigate and FinFET devices with widths and heights in the 4 to 24 nm range using a Non-Equilibrium Green's Functions approach. Electron-phonon, surface roughness and Coulomb scattering are taken into account. We show that $R_{\rm c}$ represents a significant part of the total resistance of devices with sub-30 nm gate lengths. The analysis of the quasi-Fermi level profile reveals that the spacers between the heavily doped source/drain and the gate are major contributors to the contact resistance. The conductance is indeed limited by the poor electrostatic control over the carrier density under the spacers. We then disentangle the ballistic and diffusive components of $R_{\rm c}$, and analyze the impact of different design parameters (cross section and doping profile in the contacts) on the electrical performances of the devices. The contact resistance and variability rapidly increase when the cross sectional area of the channel goes below $\simeq 50$ nm$^2$. We also highlight the role of the charges trapped at the interface between silicon and the spacer material., Comment: 16 pages, 15 figures

Quantum mechanical effects induced by the miniaturization of complementary metal-oxide-semiconductor (CMOS) technology hamper the performance and scalability prospects of field-effect transistors. However, those quantum effects, such as tunnelling and coherence, can be harnessed to use existing CMOS technology for quantum information processing. Here, we report the observation of coherent charge oscillations in a double quantum dot formed in a silicon nanowire transistor detected via its dispersive interaction with a radio-frequency resonant circuit coupled via the gate. Differential capacitance changes at the inter-dot charge transitions allow us to monitor the state of the system in the strong-driving regime where we observe the emergence of Landau-Zener-St{\"u}ckelberg-Majorana interference on the phase response of the resonator. A theoretical analysis of the dispersive signal demonstrates that quantum and tunnelling capacitance changes must be included to describe the qubit-resonator interaction. Furthermore, a Fourier analysis of the interference pattern reveals a charge coherence time, $T_2\approx 100$~ps. Our results demonstrate charge coherent control and readout in a simple silicon transistor and open up the possibility to implement charge and spin qubits in existing CMOS technology.