Driven coherent oscillations of a single electron spin in a quantum dot

Atom-by-Atom Construction of a Quantum Device

Scanning tunneling microscopes (STMs) are conventionally used to probe surfaces with atomic resolution. Recent advances in STM include tunneling from spin-polarized and superconducting tips, time-domain spectroscopy, and the fabrication of atomically precise Si nanoelectronics. In this issue of ACS Nano, Tettamanzi et al. probe a single-atom transistor in silicon, fabricated using the precision of a STM, at microwave frequencies. While previous studies have probed such devices in the MHz regime, Tettamanzi et al. probe a STM-fabricated device at GHz frequencies, which enables excited-state spectroscopy and measurements of the excited-state lifetime. The success of this experiment will enable future work on quantum control, where the wave function must be controlled on a time scale that is much shorter than the decoherence time. We review two major approaches that are being pursued to develop spin-based quantum computers and highlight some recent progress in the atom-by-atom fabrication of donor-based devices in silicon. Recent advances in STM lithography may enable practical bottom-up construction of large-scale quantum devices.

A dressed spin qubit in silicon

Coherent dressing of a quantum two-level system provides access to a new quantum system with improved properties-a different and easily tunable level splitting, faster control and longer coherence times. In our work we investigate the properties of the dressed, donor-bound electron spin in silicon, and assess its potential as a quantum bit in scalable architectures. The two dressed spin-polariton levels constitute a quantum bit that can be coherently driven with an oscillating magnetic field, an oscillating electric field, frequency modulation of the driving field or a simple detuning pulse. We measure coherence times of and , one order of magnitude longer than those of the undressed spin. Furthermore, the use of the dressed states enables coherent coupling of the solid-state spins to electric fields and mechanical oscillations.

Noncollinear Spin-Orbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot

We demonstrate experimentally that noncollinear intrinsic spin-orbit magnetic fields can be realized in a curved carbon nanotube two-segment device. Each segment, analyzed in the quantum dot regime, shows near fourfold degenerate shell structure allowing for identification of the spin-orbit coupling and the angle between the two segments. Furthermore, we determine the four unique spin directions of the quantum states for specific shells and magnetic fields. This class of quantum dot systems is particularly interesting when combined with induced superconducting correlations as it may facilitate unconventional superconductivity and detection of Cooper pair entanglement. Our device comprises the necessary elements.

Detection and control of charge states in a quintuple quantum dot

A semiconductor quintuple quantum dot with two charge sensors and an additional contact to the center dot from an electron reservoir is fabricated to demonstrate the concept of scalable architecture. This design enables formation of the five dots as confirmed by measurements of the charge states of the three nearest dots to the respective charge sensor. The gate performance of the measured stability diagram is well reproduced by a capacitance model. These results provide an important step towards realizing controllable large scale multiple quantum dot systems.

Single-Shot Ternary Readout of Two-Electron Spin States in a Quantum Dot Using Spin Filtering by Quantum Hall Edge States

We report on the single-shot readout of three two-electron spin states-a singlet and two triplet substates-whose z components of spin angular momentum are 0 and +1, in a gate-defined GaAs single quantum dot. The three spin states are distinguished by detecting spin-dependent tunnel rates that arise from two mechanisms: spin filtering by spin-resolved edge states and spin-orbital correlation with orbital-dependent tunneling. The three states form one ground state and two excited states, and we observe the spin relaxation dynamics among the three spin states.

A CMOS silicon spin qubit

Silicon, the main constituent of microprocessor chips, is emerging as a promising material for the realization of future quantum processors. Leveraging its well-established complementary metal-oxide-semiconductor (CMOS) technology would be a clear asset to the development of scalable quantum computing architectures and to their co-integration with classical control hardware. Here we report a silicon quantum bit (qubit) device made with an industry-standard fabrication process. The device consists of a two-gate, p-type transistor with an undoped channel. At low temperature, the first gate defines a quantum dot encoding a hole spin qubit, the second one a quantum dot used for the qubit read-out. All electrical, two-axis control of the spin qubit is achieved by applying a phase-tunable microwave modulation to the first gate. The demonstrated qubit functionality in a basic transistor-like device constitutes a promising step towards the elaboration of scalable spin qubit geometries in a readily exploitable CMOS platform.

Heavy-Hole States in Germanium Hut Wires

Hole spins have gained considerable interest in the past few years due to their potential for fast electrically controlled qubits. Here, we study holes confined in Ge hut wires, a so-far unexplored type of nanostructure. Low-temperature magnetotransport measurements reveal a large anisotropy between the in-plane and out-of-plane g-factors of up to 18. Numerical simulations verify that this large anisotropy originates from a confined wave function of heavy-hole character. A light-hole admixture of less than 1% is estimated for the states of lowest energy, leading to a surprisingly large reduction of the out-of-plane g-factors compared with those for pure heavy holes. Given this tiny light-hole contribution, the spin lifetimes are expected to be very long, even in isotopically nonpurified samples.

Single-electron Spin Resonance in a Quadruple Quantum Dot

Electron spins in semiconductor quantum dots are good candidates of quantum bits for quantum information processing. Basic operations of the qubit have been realized in recent years: initialization, manipulation of single spins, two qubit entanglement operations, and readout. Now it becomes crucial to demonstrate scalability of this architecture by conducting spin operations on a scaled up system. Here, we demonstrate single-electron spin resonance in a quadruple quantum dot. A few-electron quadruple quantum dot is formed within a magnetic field gradient created by a micro-magnet. We oscillate the wave functions of the electrons in the quantum dots by applying microwave voltages and this induces electron spin resonance. The resonance energies of the four quantum dots are slightly different because of the stray field created by the micro-magnet and therefore frequency-resolved addressable control of each electron spin resonance is possible.

Double-layer-gate architecture for few-hole GaAs quantum dots

We report the fabrication of single and double hole quantum dots using a double-layer-gate design on an undoped accumulation mode [Formula: see text]/GaAs heterostructure. Electrical transport measurements of a single quantum dot show varying addition energies and clear excited states. In addition, the two-level-gate architecture can also be configured into a double quantum dot with tunable inter-dot coupling.

A fault-tolerant addressable spin qubit in a natural silicon quantum dot

Fault-tolerant quantum computing requires high-fidelity qubits. This has been achieved in various solid-state systems, including isotopically purified silicon, but is yet to be accomplished in industry-standard natural (unpurified) silicon, mainly as a result of the dephasing caused by residual nuclear spins. This high fidelity can be achieved by speeding up the qubit operation and/or prolonging the dephasing time, that is, increasing the Rabi oscillation quality factor Q (the Rabi oscillation decay time divided by the π rotation time). In isotopically purified silicon quantum dots, only the second approach has been used, leaving the qubit operation slow. We apply the first approach to demonstrate an addressable fault-tolerant qubit using a natural silicon double quantum dot with a micromagnet that is optimally designed for fast spin control. This optimized design allows access to Rabi frequencies up to 35 MHz, which is two orders of magnitude greater than that achieved in previous studies. We find the optimum Q = 140 in such high-frequency range at a Rabi frequency of 10 MHz. This leads to a qubit fidelity of 99.6% measured via randomized benchmarking, which is the highest reported for natural silicon qubits and comparable to that obtained in isotopically purified silicon quantum dot-based qubits. This result can inspire contributions to quantum computing from industrial communities.

Electron Paramagnetic Resonance of Single Magnetic Moment on a Surface

We address electron spin resonance of single magnetic moments in a tunnel junction using time-dependent electric fields and spin-polarized current. We show that the tunneling current directly depends on the local magnetic moment and that the frequency of the external electric field mixes with the characteristic Larmor frequency of the local spin. The importance of the spin-polarized current induced anisotropy fields acting on the local spin moment is, moreover, demonstrated. Our proposed model thus explains the absence of an electron spin resonance for a half integer spin, in contrast with the strong signal observed for an integer spin.

A new regime of Pauli-spin blockade

Pauli-spin blockade (PSB) is a transport phenomenon in double quantum dots that allows for a type of spin to charge conversion often used to probe fundamental physics such as spin relaxation and singlet-triplet coupling. In this paper, we theoretically explore Pauli-spin blockade as a function of magnetic field B applied parallel to the substrate. In the well-studied low magnetic field regime, where PSB occurs in the forward (1, 1) → (0, 2) tunneling direction, we highlight some aspects of PSB that are not discussed in detail in existing literature, including the change in size of both bias triangles measured in the forward and reverse biasing directions as a function of B. At higher fields, we predict a crossover to "reverse PSB" in which current is blockaded in the reverse direction due to the occupation of a spin singlet as opposed to the traditional triplet blockade that occurs at low fields. The onset of reverse PSB coincides with the development of a tail like feature in the measured bias triangles and occurs when the Zeeman energy of the polarized triplet equals the exchange energy in the (0, 2) charge configuration. In Si quantum dots, these fields are experimentally accessible; thus, this work suggests a way to observe a crossover in magnetic field to qualitatively different behavior.

Spin-Orbit Coupling at the Level of a Single Electron

We utilize electron counting techniques to distinguish a spin-conserving fast tunneling process and a slower process involving spin flips in AlGaAs/GaAs-based double quantum dots. By studying the dependence of the rates on the interdot tunnel coupling of the two dots, we find that as many as 4% of the tunneling events occur with a spin flip related to spin-orbit coupling in GaAs. Our measurement has a fidelity of 99% in terms of resolving whether a tunneling event occurred with a spin flip or not.

Electron paramagnetic resonance of individual atoms on a surface

We combined the high-energy resolution of conventional spin resonance (here ~10 nano-electron volts) with scanning tunneling microscopy to measure electron paramagnetic resonance of individual iron (Fe) atoms placed on a magnesium oxide film. We drove the spin resonance with an oscillating electric field (20 to 30 gigahertz) between tip and sample. The readout of the Fe atom's quantum state was performed by spin-polarized detection of the atomic-scale tunneling magnetoresistance. We determine an energy relaxation time of T1 ≈ 100 microseconds and a phase-coherence time of T2 ≈ 210 nanoseconds. The spin resonance signals of different Fe atoms differ by much more than their resonance linewidth; in a traditional ensemble measurement, this difference would appear as inhomogeneous broadening.

Single donor electronics and quantum functionalities with advanced CMOS technology

Recent progresses in quantum dots technology allow fundamental studies of single donors in various semiconductor nanostructures. For the prospect of applications figures of merits such as scalability, tunability, and operation at relatively large temperature are of prime importance. Beyond the case of actual dopant atoms in a host crystal, similar arguments hold for small enough quantum dots which behave as artificial atoms, for instance for single spin control and manipulation. In this context, this experimental review focuses on the silicon-on-insulator devices produced within microelectronics facilities with only very minor modifications to the current industrial CMOS process and tools. This is required for scalability and enabled by shallow trench or mesa isolation. It also paves the way for real integration with conventional circuits, as illustrated by a nanoscale device coupled to a CMOS circuit producing a radio-frequency drive on-chip. At the device level we emphasize the central role of electrostatics in etched silicon nanowire transistors, which allows to understand the characteristics in the full range from zero to room temperature.

Dephasing due to Nuclear Spins in Large-Amplitude Electric Dipole Spin Resonance

We analyze effects of the hyperfine interaction on electric dipole spin resonance when the amplitude of the quantum-dot motion becomes comparable or larger than the quantum dot's size. Away from the well-known small-drive regime, the important role played by transverse nuclear fluctuations leads to a Gaussian decay with characteristic dependence on drive strength and detuning. A characterization of spin-flip gate fidelity, in the presence of such additional drive-dependent dephasing, shows that vanishingly small errors can still be achieved at sufficiently large amplitudes. Based on our theory, we analyze recent electric dipole spin resonance experiments relying on spin-orbit interactions or the slanting field of a micromagnet. We find that such experiments are already in a regime with significant effects of transverse nuclear fluctuations and the form of decay of the Rabi oscillations can be reproduced well by our theory.

Electrical Control of g-Factor in a Few-Hole Silicon Nanowire MOSFET

Hole spins in silicon represent a promising yet barely explored direction for solid-state quantum computation, possibly combining long spin coherence, resulting from a reduced hyperfine interaction, and fast electrically driven qubit manipulation. Here we show that a silicon-nanowire field-effect transistor based on state-of-the-art silicon-on-insulator technology can be operated as a few-hole quantum dot. A detailed magnetotransport study of the first accessible hole reveals a g-factor with unexpectedly strong anisotropy and gate dependence. We infer that these two characteristics could enable an electrically driven g-tensor-modulation spin resonance with Rabi frequencies exceeding several hundred mega-Hertz.

Spin-orbit interaction in bent carbon nanotubes: resonant spin transitions

We develop an effective tight-binding Hamiltonian for spin-orbit (SO) interaction in bent carbon nanotubes (CNT) for the electrons forming the π bonds between the nearest neighbor atoms. We account for the bend of the CNT and the intrinsic spin-orbit interaction which introduce mixing of π and σ bonds between the p(z) orbitals along the CNT. The effect contributes to the main origin of the SO coupling-the folding of the graphene plane into the nanotube. We discuss the bend-related contribution of the SO coupling for resonant single-electron spin and charge transitions in a double quantum dot. We report that although the effect of the bend-related SO coupling is weak for the energy spectra, it produces a pronounced increase of the spin transition rates driven by an external electric field. We find that spin-flipping transitions driven by alternate electric fields have usually larger rates when accompanied by charge shift from one dot to the other. Spin-flipping transition rates are non-monotonic functions of the driving amplitude since they are masked by stronger spin-conserving charge transitions. We demonstrate that the fractional resonances-counterparts of multiphoton transitions for atoms in strong laser fields-occurring in electrically controlled nanodevices already at moderate ac amplitudes-can be used to maintain the spin-flip transitions.

Quasiparticle spin resonance and coherence in superconducting aluminium

Conventional superconductors were long thought to be spin inert; however, there is now increasing interest in both (the manipulation of) the internal spin structure of the ground-state condensate, as well as recently observed long-lived, spin-polarized excitations (quasiparticles). We demonstrate spin resonance in the quasiparticle population of a mesoscopic superconductor (aluminium) using novel on-chip microwave detection techniques. The spin decoherence time obtained (∼100 ps), and its dependence on the sample thickness are consistent with Elliott-Yafet spin-orbit scattering as the main decoherence mechanism. The striking divergence between the spin coherence time and the previously measured spin imbalance relaxation time (∼10 ns) suggests that the latter is limited instead by inelastic processes. This work stakes out new ground for the nascent field of spin-based electronics with superconductors or superconducting spintronics.

A two-qubit logic gate in silicon

Quantum computation requires qubits that can be coupled in a scalable manner, together with universal and high-fidelity one- and two-qubit logic gates. Many physical realizations of qubits exist, including single photons, trapped ions, superconducting circuits, single defects or atoms in diamond and silicon, and semiconductor quantum dots, with single-qubit fidelities that exceed the stringent thresholds required for fault-tolerant quantum computing. Despite this, high-fidelity two-qubit gates in the solid state that can be manufactured using standard lithographic techniques have so far been limited to superconducting qubits, owing to the difficulties of coupling qubits and dephasing in semiconductor systems. Here we present a two-qubit logic gate, which uses single spins in isotopically enriched silicon and is realized by performing single- and two-qubit operations in a quantum dot system using the exchange interaction, as envisaged in the Loss-DiVincenzo proposal. We realize CNOT gates via controlled-phase operations combined with single-qubit operations. Direct gate-voltage control provides single-qubit addressability, together with a switchable exchange interaction that is used in the two-qubit controlled-phase gate. By independently reading out both qubits, we measure clear anticorrelations in the two-spin probabilities of the CNOT gate.

Quantum Manipulation of Two-Electron Spin States in Isolated Double Quantum Dots

We studied experimentally the dynamics of the exchange interaction between two antiparallel electron spins in an isolated double quantum dot where coupling to the electron reservoirs can be ignored. We demonstrate that the level of control of such a double dot is higher than in conventional double dots. In particular, it allows us to couple coherently two electron spins in an efficient manner following a scheme initially proposed by Loss and DiVincenzo [Phys. Rev. A 57, 120 (1998)]. The present study demonstrates that isolated quantum dots are a possible route to increase the number of coherently coupled quantum dots.

Electron-Hole Confinement Symmetry in Silicon Quantum Dots

We report electrical transport measurements on a gate-defined ambipolar quantum dot in intrinsic silicon. The ambipolarity allows its operation as either an electron or a hole quantum dot of which we change the dot occupancy by 20 charge carriers in each regime. Electron-hole confinement symmetry is evidenced by the extracted gate capacitances and charging energies. The results demonstrate that ambipolar quantum dots offer great potential for spin-based quantum information processing, since confined electrons and holes can be compared and manipulated in the same crystalline environment.

Measuring spin relaxation with standard pulse sequences in the singlet-triplet basis

Pulsed electrically and optically-detected magnetic resonance are extremely sensitive to changes in the permutation symmetry of weakly-coupled spin pairs, and are well-suited for investigating devices with a small number of spins. However, the change in observable from conventional electron spin resonance modifies the results of standard inductively-detected pulse sequences which are routinely used to obtain phase coherence and lifetimes. Whilst these effects have been discussed for single-pulse experiments, their role in multi-pulse sequences is less clear. Here, we investigate this effect in Hahn echo and inversion-recovery sequences, and show a second set of narrower echoes are produced that distort measurement outcomes. We demonstrate that phase cycling is able to deconvolve the additional echo signals, allowing spin relaxation times to be reliably extracted.

Charge transport through a semiconductor quantum dot-ring nanostructure

Transport properties of a gated nanostructure depend crucially on the coupling of its states to the states of electrodes. In the case of a single quantum dot the coupling, for a given quantum state, is constant or can be slightly modified by additional gating. In this paper we consider a concentric dot-ring nanostructure (DRN) and show that its transport properties can be drastically modified due to the unique geometry. We calculate the dc current through a DRN in the Coulomb blockade regime and show that it can efficiently work as a single-electron transistor (SET) or a current rectifier. In both cases the transport characteristics strongly depend on the details of the confinement potential. The calculations are carried out for low and high bias regime, the latter being especially interesting in the context of current rectification due to fast relaxation processes.

Perspective: Stimulated Raman adiabatic passage: The status after 25 years

The first presentation of the STIRAP (stimulated Raman adiabatic passage) technique with proper theoretical foundation and convincing experimental data appeared 25 years ago, in the May 1st, 1990 issue of The Journal of Chemical Physics. By now, the STIRAP concept has been successfully applied in many different fields of physics, chemistry, and beyond. In this article, we comment briefly on the initial motivation of the work, namely, the study of reaction dynamics of vibrationally excited small molecules, and how this initial idea led to the documented success. We proceed by providing a brief discussion of the physics of STIRAP and how the method was developed over the years, before discussing a few examples from the amazingly wide range of applications which STIRAP now enjoys, with the aim to stimulate further use of the concept. Finally, we mention some promising future directions.

Exciton Fine-Structure Splitting in Self-Assembled Lateral InAs/GaAs Quantum-Dot Molecular Structures

Fine-structure splitting (FSS) of excitons in semiconductor nanostructures is a key parameter that has significant implications in photon entanglement and polarization conversion between electron spins and photons, relevant to quantum information technology and spintronics. Here, we investigate exciton FSS in self-organized lateral InAs/GaAs quantum-dot molecular structures (QMSs) including laterally aligned double quantum dots (DQDs), quantum-dot clusters (QCs), and quantum rings (QRs), by employing polarization-resolved microphotoluminescence (μPL) spectroscopy. We find a clear trend in FSS between the studied QMSs depending on their geometric arrangements, from a large FSS in the DQDs to a smaller FSS in the QCs and QRs. This trend is accompanied by a corresponding difference in the optical polarization directions of the excitons between these QMSs, namely, the bright-exciton lines are linearly polarized preferably along or perpendicular to the [11̅0] crystallographic axis in the DQDs that also defines the alignment direction of the two constituting QDs, whereas in the QCs and QRs, the polarization directions are randomly oriented. We attribute the observed trend in the FSS to a significant reduction of the asymmetry in the lateral confinement potential of the excitons in the QRs and QCs as compared with the DQDs, as a result of a compensation between the effects of lateral shape anisotropy and piezoelectric field. Our work demonstrates that FSS strongly depends on the geometric arrangements of the QMSs, which effectively tune the degree of the compensation effects and are capable of reducing FSS even in a strained QD system to a limit similar to strain-free QDs. This approach provides a pathway in obtaining high-symmetry quantum emitters desirable for realizing photon entanglement and spintronic devices based on such nanostructures, utilizing an uninterrupted epitaxial growth procedure without special requirements for lattice-matched materials combinations, specific substrate orientations, and nanolithography.

Dynamic creation of a topologically-ordered Hamiltonian using spin-pulse control in the Heisenberg model

Hamiltonian engineering is an important approach for quantum information processing, when appropriate materials do not exist in nature or are unstable. So far there is no stable material for the Kitaev spin Hamiltonian with anisotropic interactions on a honeycomb lattice, which plays a crucial role in the realization of both Abelian and non-Abelian anyons. Here, we show two methods to dynamically realize the Kitaev spin Hamiltonian from the conventional Heisenberg spin Hamiltonian using pulse-control techniques based on the Baker-Campbell-Hausdorff (BCH) formula. In the first method, the Heisenberg interaction is changed into Ising interactions in the first process of the pulse sequence. In the next process of the first method, we transform them to a desirable anisotropic Kitaev spin Hamiltonian. In the second more efficient method, we show that if we carefully design two-dimensional pulses that vary depending on the qubit location, we can obtain the desired Hamiltonian in only one step of applying the BCH formula. As an example, we apply our methods to spin qubits based on quantum dots, in which the effects of both the spin-orbit interaction and the hyperfine interaction are estimated.

Broadband electrically detected magnetic resonance using adiabatic pulses

We present a broadband microwave setup for electrically detected magnetic resonance (EDMR) based on microwave antennae with the ability to apply arbitrarily shaped pulses for the excitation of electron spin resonance (ESR) and nuclear magnetic resonance (NMR) of spin ensembles. This setup uses non-resonant stripline structures for on-chip microwave delivery and is demonstrated to work in the frequency range from 4 MHz to 18 GHz. π pulse times of 50 ns and 70 μs for ESR and NMR transitions, respectively, are achieved with as little as 100 mW of microwave or radiofrequency power. The use of adiabatic pulses fully compensates for the microwave magnetic field inhomogeneity of the stripline antennae, as demonstrated with the help of BIR4 unitary rotation pulses driving the ESR transition of neutral phosphorus donors in silicon and the NMR transitions of ionized phosphorus donors as detected by electron nuclear double resonance (ENDOR).

Subdecoherence time generation and detection of orbital entanglement in quantum dots

Recent experiments have demonstrated subdecoherence time control of individual single-electron orbital qubits. Here we propose a quantum-dot-based scheme for generation and detection of pairs of orbitally entangled electrons on a time scale much shorter than the decoherence time. The electrons are entangled, via two-particle interference, and transferred to the detectors during a single cotunneling event, making the scheme insensitive to charge noise. For sufficiently long detector dot lifetimes, cross-correlation detection of the dot charges can be performed with real-time counting techniques, providing for an unambiguous short-time Bell inequality test of orbital entanglement.

Coherent dynamics of a telecom-wavelength entangled photon source

Quantum networks can interconnect remote quantum information processors, allowing interaction between different architectures and increasing net computational power. Fibre-optic telecommunications technology offers a practical platform for routing weakly interacting photonic qubits, allowing quantum correlations and entanglement to be established between distant nodes. Although entangled photons have been produced at telecommunications wavelengths using spontaneous parametric downconversion in nonlinear media, as system complexity increases their inherent excess photon generation will become limiting. Here we demonstrate entangled photon pair generation from a semiconductor quantum dot at a telecommunications wavelength. Emitted photons are intrinsically anti-bunched and violate Bell's inequality by 17 standard deviations High-visibility oscillations of the biphoton polarization reveal the time evolution of the emitted state with exceptional clarity, exposing long coherence times. Furthermore, we introduce a method to evaluate the fidelity to a time-evolving Bell state, revealing entanglement between photons emitted up to 5 ns apart, exceeding the exciton lifetime.

Microwave-driven coherent operation of a semiconductor quantum dot charge qubit

An intuitive realization of a qubit is an electron charge at two well-defined positions of a double quantum dot. This qubit is simple and has the potential for high-speed operation because of its strong coupling to electric fields. However, charge noise also couples strongly to this qubit, resulting in rapid dephasing at all but one special operating point called the 'sweet spot'. In previous studies d.c. voltage pulses have been used to manipulate semiconductor charge qubits but did not achieve high-fidelity control, because d.c. gating requires excursions away from the sweet spot. Here, by using resonant a.c. microwave driving we achieve fast (greater than gigahertz) and universal single qubit rotations of a semiconductor charge qubit. The Z-axis rotations of the qubit are well protected at the sweet spot, and we demonstrate the same protection for rotations about arbitrary axes in the X-Y plane of the qubit Bloch sphere. We characterize the qubit operation using two tomographic approaches: standard process tomography and gate set tomography. Both methods consistently yield process fidelities greater than 86% with respect to a universal set of unitary single-qubit operations.

Suppression of nuclear spin bath fluctuations in self-assembled quantum dots induced by inhomogeneous strain

Interaction with nuclear spins leads to decoherence and information loss in solid-state electron-spin qubits. One particular, ineradicable source of electron decoherence arises from decoherence of the nuclear spin bath, driven by nuclear-nuclear dipolar interactions. Owing to its many-body nature nuclear decoherence is difficult to predict, especially for an important class of strained nanostructures where nuclear quadrupolar effects have a significant but largely unknown impact. Here, we report direct measurement of nuclear spin bath coherence in individual self-assembled InGaAs/GaAs quantum dots: spin-echo coherence times in the range 1.2-4.5 ms are found. Based on these values, we demonstrate that strain-induced quadrupolar interactions make nuclear spin fluctuations much slower compared with lattice-matched GaAs/AlGaAs structures. Our findings demonstrate that quadrupolar effects can potentially be used to engineer optically active III-V semiconductor spin-qubits with a nearly noise-free nuclear spin bath, previously achievable only in nuclear spin-0 semiconductors, where qubit network interconnection and scaling are challenging.

Synthesis and enhanced fluorescence of Ag doped CdTe semiconductor quantum dots

Doping with intentional impurities is an intriguing way to tune the properties of semiconductor nanocrystals. However, the synthesis of some specific doped semiconductor nanocrystals remains a challenge and the doping mechanism in this strongly confined system is still not clearly understood. In this work, we report, for the first time, the synthesis of stable and water-soluble Ag-doped CdTe semiconductor quantum dots (SQDs) via a facile aqueous approach. Experimental characterization demonstrated the efficient doping of the Ag impurities into the CdTe SQDs with an appropriate reaction time. By doping 0.3% Ag impurities, the Stokes shift is decreased by 120 meV, the fluorescence intensity is enhanced more than 3 times, the radiative rate is enhanced 4.2 times, and the non-radiative rate is efficiently suppressed. These observations reveal that the fluorescence enhancement in Ag-doped CdTe SQDs is mainly attributed to the minimization of surface defects, filling of the trap states, and the enhancement of the radiative rate by the silver dopants. Our results suggest that the silver doping is an efficient method for tuning the optical properties of the CdTe SQDs.

Manipulating carriers' spin polarization in the Heusler alloy Mn2CoAl

We report that complete spin polarization and controllable spin polarization of carriers can be simultaneously realized in the Heusler alloy Mn₂CoAl simply by applying external pressures based on first-principles studies.

Fast electrical control of single electron spins in quantum dots with vanishing influence from nuclear spins

We demonstrate fast universal electrical spin manipulation with inhomogeneous magnetic fields. With fast Rabi frequency up to 127 MHz, we leave the conventional regime of strong nuclear-spin influence and observe a spin-flip fidelity >96%, a distinct chevron Rabi pattern in the spectral-time domain, and a spin resonance linewidth limited by the Rabi frequency, not by the dephasing rate. In addition, we establish fast z rotations up to 54 MHz by directly controlling the spin phase. Our findings will significantly facilitate tomography and error correction with electron spins in quantum dots.

Ultrafast generation of pseudo-magnetic field for valley excitons in WSe2monolayers

The valley pseudospin is a degree of freedom that emerges in atomically thin two-dimensional transition metal dichalcogenides (MX2). The capability to manipulate it, in analogy to the control of spin in spintronics, can open up exciting opportunities. Here, we demonstrate that an ultrafast and ultrahigh valley pseudo-magnetic field can be generated by using circularly polarized femtosecond pulses to selectively control the valley degree of freedom in monolayer MX2.Using ultrafast pump-probe spectroscopy, we observed a pure and valley-selective optical Stark effect in WSe2monolayers from the nonresonant pump, resulting in an energy splitting of more than 10 milli–electron volts between the K and K′ valley exciton transitions. Our study opens up the possibility to coherently manipulate the valley polarization for quantum information applications.

Nanoscale spin rectifiers controlled by the Stark effect

The control of orbitals and spin states of single electrons is a key ingredient for quantum information processing and novel detection schemes and is, more generally, of great relevance for spintronics. Coulomb and spin blockade in double quantum dots enable advanced single-spin operations that would be available even for room-temperature applications with sufficiently small devices. To date, however, spin operations in double quantum dots have typically been observed at sub-kelvin temperatures, a key reason being that it is very challenging to scale a double quantum dot system while retaining independent field-effect control of individual dots. Here, we show that the quantum-confined Stark effect allows two dots only 5 nm apart to be independently addressed without the requirement for aligned nanometre-sized local gating. We thus demonstrate a scalable method to fully control a double quantum dot device, regardless of its physical size. In the present implementation we present InAs/InP nanowire double quantum dots that display an experimentally detectable spin blockade up to 10 K. We also report and discuss an unexpected re-entrant spin blockade lifting as a function of the magnetic field intensity.

An addressable quantum dot qubit with fault-tolerant control-fidelity

Exciting progress towards spin-based quantum computing has recently been made with qubits realized using nitrogen-vacancy centres in diamond and phosphorus atoms in silicon. For example, long coherence times were made possible by the presence of spin-free isotopes of carbon and silicon. However, despite promising single-atom nanotechnologies, there remain substantial challenges in coupling such qubits and addressing them individually. Conversely, lithographically defined quantum dots have an exchange coupling that can be precisely engineered, but strong coupling to noise has severely limited their dephasing times and control fidelities. Here, we combine the best aspects of both spin qubit schemes and demonstrate a gate-addressable quantum dot qubit in isotopically engineered silicon with a control fidelity of 99.6%, obtained via Clifford-based randomized benchmarking and consistent with that required for fault-tolerant quantum computing. This qubit has dephasing time T2* = 120 μs and coherence time T2 = 28 ms, both orders of magnitude larger than in other types of semiconductor qubit. By gate-voltage-tuning the electron g*-factor we can Stark shift the electron spin resonance frequency by more than 3,000 times the 2.4 kHz electron spin resonance linewidth, providing a direct route to large-scale arrays of addressable high-fidelity qubits that are compatible with existing manufacturing technologies.

Coherent Precession of an Individual 5/2 Spin

We present direct observation of a coherent spin precession of an individual Mn^{2+} ion, having both electronic and nuclear spins equal to 5/2, embedded in a CdTe quantum dot and placed in a magnetic field. The spin state evolution is probed in a time-resolved pump-probe measurement of absorption of the single dot. The experiment reveals subtle details of the large-spin coherent dynamics, such as nonsinusoidal evolution of states occupation, and beatings caused by the strain-induced differences in energy levels separation. Sensitivity of the large-spin impurity on the crystal strain opens the possibility of using it as a local strain probe.

Principles and application of heterodyne scanning tunnelling spectroscopy

Detection of the extremely weak signals in spectroscopy over an extremely wide frequency region is central to diverse sciences, including materials science, biology, astronomy and chemistry. Here we show a new type of atomic-scale spectroscopy, heterodyne scanning tunnelling spectroscopy (HSTS), which is based on the innovative application of the nonlinear heterodyne-mixing detection at the metal-insulator-metal (MIM) heterojunction of STM tip–vacuum–sample. The principle of HSTS is identical to that of the Atacama Large Millimeter Array (ALMA) space telescope in terms of using heterojunction for detecting extremely weak signals by converting from terahertz region to lower frequency regions. The MIM detector of ALMA, which is composed of niobium–titanium–nitride (NbTiN) tip-insulator-NbTiN, is very similar in shape and size to that of HSTS. We successfully detect a heterodyne beat signal f₃ (= |f₂ − f₁|) and intermodulation distortion via tunnelling current by superimposing two different AC signals, f₁ and f₂, onto the DC tunnelling current at a highly oriented pyrolytic graphite (HOPG) surface. We then obtain spectra of the localized electronic states of HOPG by using f₃. HSTS can be performed with a high resolution and over a wide energy range, including the terahertz range.

Quantum teleportation of laser-generated photons with an entangled-light-emitting diode

Quantum teleportation can transfer information between physical systems, which is essential for engineering quantum networks. Of the many technologies being investigated to host quantum bits, photons have obvious advantages as 'pure' quantum information carriers, but their bandwidth and energy is determined by the quantum system that generates them. Here we show that photons from fundamentally different sources can be used in the optical quantum teleportation protocol. The sources we describe have bandwidth differing by a factor over 100, but we still observe teleportation with average fidelity of 0.77, beating the quantum limit by 10 standard deviations. Furthermore, the dissimilar nature of our sources exposes physics hidden in previous experiments, which we also predict numerically. These phenomena include converting qubits from Poissonian to Fock statistics, quantum interference, beats and teleportation for spectrally non-degenerate photons, and acquisition of evolving character following teleportation of a qubit.

Counter-diabatic driving for fast spin control in a two-electron double quantum dot

The techniques of shortcuts to adiabaticity have been proposed to accelerate the "slow" adiabatic processes in various quantum systems with the applications in quantum information processing. In this paper, we study the counter-diabatic driving for fast adiabatic spin manipulation in a two-electron double quantum dot by designing time-dependent electric fields in the presence of spin-orbit coupling. To simplify implementation and find an alternative shortcut, we further transform the Hamiltonian in term of Lie algebra, which allows one to use a single Cartesian component of electric fields. In addition, the relation between energy and time is quantified to show the lower bound for the operation time when the maximum amplitude of electric fields is given. Finally, the fidelity is discussed with respect to noise and systematic errors, which demonstrates that the decoherence effect induced by stochastic environment can be avoided in speeded-up adiabatic control.

Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot

Nanofabricated quantum bits permit large-scale integration but usually suffer from short coherence times due to interactions with their solid-state environment. The outstanding challenge is to engineer the environment so that it minimally affects the qubit, but still allows qubit control and scalability. Here, we demonstrate a long-lived single-electron spin qubit in a Si/SiGe quantum dot with all-electrical two-axis control. The spin is driven by resonant microwave electric fields in a transverse magnetic field gradient from a local micromagnet, and the spin state is read out in the single-shot mode. Electron spin resonance occurs at two closely spaced frequencies, which we attribute to two valley states. Thanks to the weak hyperfine coupling in silicon, a Ramsey decay timescale of 1 μs is observed, almost two orders of magnitude longer than the intrinsic timescales in GaAs quantum dots, whereas gate operation times are comparable to those reported in GaAs. The spin echo decay time is ~40 μs, both with one and four echo pulses, possibly limited by intervalley scattering. These advances strongly improve the prospects for quantum information processing based on quantum dots.

Electron spin separation without magnetic field

A nanodevice capable of separating spins of two electrons confined in a quantum dot formed in a gated semiconductor nanowire is proposed. Two electrons confined initially in a single quantum dot in the singlet state are transformed into the system of two electrons confined in two spatially separated quantum dots with opposite spins. In order to separate the electrons' spins we exploit transitions between the singlet and the triplet state, which are induced by resonantly oscillating Rashba spin-orbit coupling strength. The proposed device is all electrically controlled and the electron spin separation can be realized within tens of picoseconds. The results are supported by solving numerically the quasi-one-dimensional time-dependent Schroedinger equation for two electrons, where the electron-electron correlations are taken into account in the exact manner.

Electrically driven nuclear spin resonance in single-molecule magnets

Recent advances in addressing isolated nuclear spins have opened up a path toward using nuclear-spin-based quantum bits. Local magnetic fields are normally used to coherently manipulate the state of the nuclear spin; however, electrical manipulation would allow for fast switching and spatially confined spin control. Here, we propose and demonstrate coherent single nuclear spin manipulation using electric fields only. Because there is no direct coupling between the spin and the electric field, we make use of the hyperfine Stark effect as a magnetic field transducer at the atomic level. This quantum-mechanical process is present in all nuclear spin systems, such as phosphorus or bismuth atoms in silicon, and offers a general route toward the electrical control of nuclear-spin-based devices.

Large modulation of zero-dimensional electronic states in quantum dots by electric-double-layer gating

Electrical manipulation and read-out of quantum states in zero-dimensional nanostructures by nano-gap metal electrodes is expected to bring about innovation in quantum information processing. However, electrical tunability of the quantum states in zero-dimensional nanostructures is limited by the screening of gate electric fields. Here we demonstrate a new way to realize wide-range electrical modulation of quantum states of single self-assembled InAs quantum dots (QDs) with a liquid-gated electric-double-layer (EDL) transistor geometry. The efficiency of EDL gating is 6-90 times higher than that of the conventional solid gating. The quantized energy level spacing is modulated from ~15 to ~25 meV, and the electron g-factor is electrically tuned over a wide range. Such a field effect tuning can be explained by the modulation in the confinement potential of electrons in the QDs. The EDL gating on the QDs also provides potential compatibility with optical manipulation of single-electron charge/spin states.

Hole spin coherence in a Ge/Si heterostructure nanowire

Relaxation and dephasing of hole spins are measured in a gate-defined Ge/Si nanowire double quantum dot using a fast pulsed-gate method and dispersive readout. An inhomogeneous dephasing time T2* 0.18 μs exceeds corresponding measurements in III–V semiconductors by more than an order of magnitude, as expected for predominately nuclear-spin-free materials. Dephasing is observed to be exponential in time, indicating the presence of a broadband noise source, rather than Gaussian, previously seen in systems with nuclear-spin-dominated dephasing.

Extreme harmonic generation in electrically driven spin resonance

We report the observation of multiple harmonic generation in electric dipole spin resonance in an InAs nanowire double quantum dot. The harmonics display a remarkable detuning dependence: near the interdot charge transition as many as eight harmonics are observed, while at large detunings we only observe the fundamental spin resonance condition. The detuning dependence indicates that the observed harmonics may be due to Landau-Zener transition dynamics at anticrossings in the energy level spectrum.