In this work we perform direct single-shot readout of the singlet-triplet states in exchange coupled electrons confined to precision placed donor atoms in silicon. Our method takes advantage of the large energy splitting given by the Pauli-spin blockaded (2,0) triplet states, from which we can achieve a single-shot readout fidelity of 98.4$\pm$0.2%. We measure the triplet-minus relaxation time to be of the order 3s at 2.5T and observe its predicted decrease as a function of magnetic field, reaching 0.5s at 1T.
Electron readout contrast enhancement in the parallel nuclear regime of an exchange-coupled donor spin qubit system
Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室）；Quantum Machines（量子机器公司）；Intel Corporation（英特尔公司）；School of Electrical Engineering and Telecommunications, UNSW Sydney（新南威尔士大学悉尼分校电气与电信工程学院）；ARC Centre of Excellence for Quantum Computation and Communication Technology（ARC量子计算与通信技术卓越中心）；Diraq Pty. Ltd.（Diraq有限公司）；School of Fundamental Science and Technology, Keio University（庆应义塾大学基础科学与技术学院）；School of Physics, University of Melbourne（墨尔本大学物理学院）；School of Science, RMIT University（皇家墨尔本理工大学理学院）
Nuclear spins show long coherence times and are well isolated from the environment, which are properties making them promising for quantum information applications. Here, we present a method for nuclear spin readout by probing the transmission of a microwave resonator. We consider a single electron in a silicon quantum dot-donor device interacting with a microwave resonator via the electric dipole coupling and subjected to a homogeneous magnetic field and a transverse magnetic field gradient. In our scenario, the electron spin interacts with a $^{31}\mathrm{P}$ defect nuclear spin via the hype…
Substitutional donor atoms in silicon are promising qubits for quantum computation with extremely long relaxation and dephasing times demonstrated. One of the critical challenges of scaling these systems is determining inter-donor distances to achieve controllable wavefunction overlap while at the same time performing high fidelity spin readout on each qubit. Here we achieve such a device by means of scanning tunnelling microscopy lithography. We measure anti-correlated spin states between two donor-based spin qubits in silicon separated by 16${\pm}1$ nm. By utilizing an asymmetric system with…
We describe a method to control and detect in single-shot the electron spin state of an individual donor in silicon with greatly enhanced sensitivity. A silicon-based Single-Electron Transistor (SET) allows for spin-dependent tunneling of the donor electron directly into the SET island during the read-out phase. Simulations show that the charge transfer signals are typically Δq > 0.2 e - over an order of magnitude larger than achievable with metallic SETs on the SiO2 surface. A complete spin-based qubit structure is obtained by adding a local Electron Spin Resonance line for coherent spin cont…
Electrical detection of spins is an essential tool in understanding the dynamics of spins in semiconductor devices, providing valuable insights for applications ranging from optoelectronics and spintronics to quantum information processing. For electron spins bound to shallow donors in silicon, bulk electrically-detected magnetic resonance has relied on coupling to spin readout partners such as paramagnetic defects or conduction electrons which fundamentally limits spin coherence times. Here we demonstrate electrical detection of phosphorus donor electron spin resonance by transport through a …
Opto-Electrical Detection of Donor Bound Excitons in Silicon-on-Insulator Substrate
University of Jyväskylä（于韦斯屈莱大学）；QuTech（奎泰克）；Netherlands Organisation for Applied Scientific Research (TNO)（荷兰应用科学研究组织）；Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学卡弗里纳米科学研究所）
Donor impurity spins in silicon-28 are highly competitive qubits for upcoming solid-state quantum technologies, yet a proven scalable strategy for multi-qubit devices remains conspicuously absent. These CMOS-compatible, atomically identical qubits offer significant advantages including 3-hour coherence ($T_2$) lifetimes, as well as simultaneous qubit initialization, manipulation and readout fidelities near $\sim\!99.9\%$. These properties meet the requirements for many modern quantum error correction protocols, which are essential for constructing large-scale universal quantum technologies. Ho…
We compare charge transitions on a deterministic single P donor in silicon using radio frequency reflectometry measurements with a tunnel coupled reservoir and DC charge sensing using a capacitively coupled single electron transistor (SET). By measuring the conductance through the SET and comparing this with the phase shift of the reflected RF excitation from the reservoir, we can discriminate between charge transfer within the SET channel and tunneling between the donor and reservoir. The RF measurement allows observation of donor electron transitions at every charge degeneracy point in contr…
Shifts from the expected nuclear magnetic resonance frequencies of antimony and bismuth donors in silicon of greater than a megahertz are observed in electrically detected magnetic resonance spectra. Defects created by ion implantation of the donors are discussed as the source of effective electric field gradients generating these shifts via quadrupole interaction with the nuclear spins. The experimental results are modeled quantitatively by molecular orbital theory for a coupled pair consisting of a donor and a spin-dependent recombination readout center.
Donor spin states in silicon are a promising candidate for quantum information processing. One possible donor spin readout mechanism is the bound exciton transition that can be excited optically and creates an electrical signal when it decays. This transition has been extensively studied in bulk, but in order to scale towards localized spin readout, microfabricated structures are needed for detection. As these electrodes will inevitably cause strain in the silicon lattice, it will be crucial to understand how strain affects the exciton transitions. Here we study the phosphorous donor bound exc…
The readout of semiconductor spin qubits based on spin blockade is fast but suffers from a small charge signal. Previous work suggested large benefits from additional charge mapping processes, however uncertainties remain about the underlying mechanisms and achievable fidelity. In this work, we study the single-shot fidelity and limiting mechanisms for two variations of an enhanced latching readout. We achieve average single-shot readout fidelities > 99.3% and > 99.86% for the conventional and enhanced readout respectively, the latter being the highest to date for spin blockade. The signal amp…
We measure singlet-triplet mixing in a precision fabricated double donor dot comprising of 2 and 1 phosphorus atoms separated by $16{\pm}1$ nm. We identify singlet and triplet-minus states by performing sequential independent spin readout of the two electron system and probe its dependence on magnetic field strength. The relaxation of singlet and triplet states are measured to be $12.4{\pm}1.0$ s and $22.1{\pm}1.0$ s respectively at $B_z{=}2.5$ T.
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.
We consider a quantum network of mid-infrared, graphene plasmons coupled to the hydrogen-like excited states of group-V donors in silicon. First, we show how to use plasmon-enhanced light-matter interactions to achieve single-shot spin readout of the donor qubits via optical excitation and electrical detection of the emitted plasmons. We then show how plasmons in high mobility graphene nanoribbons can be used to achieve high-fidelity, two-qubit gates and entanglement of distant Si donor qubits. The proposed device is readily compatible with existing technology and fabrication methods.
For solid-state spin qubits, single-gate RF readout can help minimise the number of gates required for scale-up to many qubits since the readout sensor can integrate into the existing gates required to manipulate the qubits (Veldhorst 2017, Pakkiam 2018). However, a key requirement for a scalable quantum computer is that we must be capable of resolving the qubit state within single-shot, that is, a single measurement (DiVincenzo 2000). Here we demonstrate single-gate, single-shot readout of a singlet-triplet spin state in silicon, with an average readout fidelity of $82.9\%$ at a $3.3~\text{kH…
Last year, Salfi et al. made the first direct measurements of a donor wave function and found extremely good theoretical agreement with atomistic tight-binding [Salfi et al., Nat. Mater. 13, 605 (2014)]. Here, we show that multi-valley effective mass theory, applied properly, does achieve close agreement with tight-binding and hence gives reliable predictions. To demonstrate this, we variationally solve the coupled six-valley Shindo-Nara equations, including silicon's full Bloch functions. Surprisingly, we find that including the full Bloch functions necessitates a tetrahedral, rather than sph…
A single nuclear spin holds the promise of being a long-lived quantum bit or quantum memory, with the high fidelities required for fault-tolerant quantum computing. We show here that such promise could be fulfilled by a single phosphorus (31P) nuclear spin in a silicon nanostructure. By integrating single-shot readout of the electron spin with on-chip electron spin resonance, we demonstrate the quantum non-demolition, electrical single-shot readout of the nuclear spin, with readout fidelity better than 99.8% - the highest for any solid-state qubit. The single nuclear spin is then operated as a…
We propose a quantum computer architecture involving substitutional donors in photonic-crystal silicon cavities and the optical initialization, manipulation, and detection processes already demonstrated in ion traps and other atomic systems. Our scheme considerably simplifies the implementation of the building blocks for the successful operation of silicon-based solid-state quantum computers, including positioning of the donors, realization of one- and two-qubit gates, initialization and readout of the qubits. Detailed consideration of the processes involved, using state-of-the-art values for …
We report fabrication of transistors in a FinFET geometry using isotopically purified silicon-28 -on-insulator (28-SOI) substrates. Donor electron spin coherence in natural silicon is limited by spectral diffusion due to the residual $^{29}$Si nuclear spin bath, making isotopically enriched nuclear spin-free $^{28}$Si substrates a promising candidate for forming spin quantum bit devices. The FinFET architecture is fully compatible with single-ion implant detection for donor-based qubits, and the donor spin-state readout through electrical detection of spin resonance. We describe device process…
Two-electron states bound to donors in silicon are important for both two qubit gates and spin readout. We present a full configuration interaction technique in the atomistic tight-binding basis to capture multi-electron exchange and correlation effects taking into account the full bandstructure of silicon and the atomic scale granularity of a nanoscale device. Excited $s$-like states of $A_1$-symmetry are found to strongly influence the charging energy of a negative donor centre. We apply the technique on sub-surface dopants subjected to gate electric fields, and show that bound triplet state…
We have studied the coherent spin dynamics in an oblique magnetic field of electrons localized on donors and placed in the middle of a single CdTe quantum well, by using a time-resolved optical technique: the photo-induced Faraday rotation. We showed that this dynamics is affected by a weak Overhauser field created via the hyperfine interaction of optically spin-polarized donor-bound electrons with the surrounding nuclear isotopes carrying non-zero spins. We have measured this nuclear field, which is on the order of a few mT and can reach a maximum experimental value of 9.4 mT. This value repr…
We demonstrate radio frequency (RF) readout of electrically detected magnetic resonance in phosphorus-doped silicon metal-oxide field-effecttransistors (MOSFETs), operated at liquid helium temperatures. For the first time, the Si:P hyperfine lines have been observed using radio frequency reflectometry, which is promising for high-bandwidth operation and possibly time-resolved detection of spin resonance in donor-based semiconductor devices. Here we present the effect of microwave (MW) power and MOSFET biasing conditions on the EDMR signals.
We present the experimental observation of a large exchange coupling $J \approx 300$ $μ$eV between two $^{31}$P electron spin qubits in silicon. The singlet and triplet states of the coupled spins are monitored in real time by a Single-Electron Transistor, which detects ionization from tunnel-rate-dependent processes in the coupled spin system, yielding single-shot readout fidelities above 95%. The triplet to singlet relaxation time $T_1 \approx 4$ ms at zero magnetic field agrees with the theoretical prediction for $J$-coupled $^{31}$P dimers in silicon. The time evolution of the 2-electron s…
The scattering of conduction electrons off neutral donors depends sensitively on the relative orientation of their spin states. We present a theory of spin-dependent scattering in the two dimensional electron gas (2DEG) of field effect transistors. Our theory shows that the scattering mechanism is dominated by virtual transitions to negatively ionized donor levels. This effect translates into a source-drain current that always gets reduced when donor spins are at resonance with a strong microwave field. We propose a model for donor impurities interacting with conduction electrons in a silicon …
Germanium has emerged as an exceptionally promising material for spintronics and quantum information applications, with significant fundamental advantages over silicon. However, efforts to create atomic-scale devices using donor atoms as qubits have largely focussed on phosphorus in silicon. Positioning phosphorus in silicon with atomic-scale precision requires a thermal incorporation anneal, but the low success rate for this step has been shown to be a fundamental limitation prohibiting the scale-up to large-scale devices. Here, we present a comprehensive study of arsine (AsH$_3$) on the germ…
The size of silicon transistors used in microelectronic devices is shrinking to the level where quantum effects become important. While this presents a significant challenge for the further scaling of microprocessors, it provides the potential for radical innovations in the form of spin-based quantum computers and spintronic devices. An electron spin in Si can represent a well-isolated quantum bit with long coherence times because of the weak spin-orbit coupling and the possibility to eliminate nuclear spins from the bulk crystal. However, the control of single electrons in Si has proved chall…
Phosphorus donor spins in silicon offer a number of promising characteristics for the implementation of robust qubits. Amongst various concepts for scale-up, the shared-control concept takes advantage of 3D scanning tunnelling microscope (STM) fabrication techniques to minimise the number of control lines, allowing the donors to be placed at the pitch limit of $\geq$30 nm, enabling dipole interactions. A fundamental challenge is to exploit the faster exchange interaction, however, the donor spacings required are typically 15 nm or less, and the exchange interaction is notoriously sensitive to …
Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements only indirectly probe wavefunc…
We propose and analyse a method for single shot measurement of the total spin of a two electron system in a coupled quantum dot or donor impurity structure, which can be used for readout in a quantum computer. The spin can be inferred by observing spin dependent fluctuations of charge between the two sites, via a nearby electrometer. Realistic experimental parameters indicate that the fidelity of the measurement can be larger than 0.9999 with existing or near-future technology.
Electron spins are amongst the most coherent solid-state systems known, however, to be used in devices for quantum sensing and information processing applications, they must be typically placed near interfaces. Understanding and mitigating the impacts of such interfaces on the coherence and spectral properties of electron spins is critical to realize such applications, but is also challenging: inferring such data from single-spin studies requires many measurements to obtain meaningful results, while ensemble measurements typically give averaged results that hide critical information. Here, we …
Building upon the demonstration of coherent control and single-shot readout of the electron and nuclear spins of individual 31-P atoms in silicon, we present here a systematic experimental estimate of quantum gate fidelities using randomized benchmarking of 1-qubit gates in the Clifford group. We apply this analysis to the electron and the ionized 31-P nucleus of a single P donor in isotopically purified 28-Si. We find average gate fidelities of 99.95 % for the electron, and 99.99 % for the nuclear spin. These values are above certain error correction thresholds, and demonstrate the potential …
We investigate the effect of the position of the donor in the quantum well on the energy spectrum and the oscillator strength of the D- system in the presence of a perpendicular magnetic field. As a function of the magnetic field we find that when the D- centers are placed sufficiently off-center they undergo singlet-triplet transitions which are similar to those found in many-electron parabolic quantum dots. The main difference is that the number of such transitions depends on the position of the donor and only a finite number of such singlet-triplet transitions are found as function of the s…
We demonstrate humidity sensing using a change of electrical resistance of a single- layer chemical vapor deposited (CVD) graphene that is placed on top of a SiO2 layer on a Si wafer. To investigate the selectivity of the sensor towards the most common constituents in air, its signal response was characterized individually for water vapor (H2O), nitrogen (N2), oxygen (O2), and argon (Ar). In order to assess the humidity sensing effect for a range from 1% relative humidity (RH) to 96% RH, devices were characterized both in a vacuum chamber and in a humidity chamber at atmospheric pressure. The …
A single atom is the prototypical quantum system, and a natural candidate for a quantum bit - the elementary unit of a quantum computer. Atoms have been successfully used to store and process quantum information in electromagnetic traps, as well as in diamond through the use of the NV-center point defect. Solid state electrical devices possess great potential to scale up such demonstrations from few-qubit control to larger scale quantum processors. In this direction, coherent control of spin qubits has been achieved in lithographically-defined double quantum dots in both GaAs and Si. However, …
