Roadmap on quantum nanotechnologies.

Quantum phenomena are typically observable at length and time scales smaller than those of our everyday experience, often involving individual particles or excitations. The past few decades have seen a revolution in the ability to structure matter at the nanoscale, and experiments at the single particle level have become commonplace. This has opened wide new avenues for exploring and harnessing quantum mechanical effects in condensed matter. These quantum phenomena, in turn, have the potential to revolutionize the way we communicate, compute and probe the nanoscale world. Here, we review developments in key areas of quantum research in light of the nanotechnologies that enable them, with a view to what the future holds. Materials and devices with nanoscale features are used for quantum metrology and sensing, as building blocks for quantum computing, and as sources and detectors for quantum communication. They enable explorations of quantum behaviour and unconventional states in nano- and opto-mechanical systems, low-dimensional systems, molecular devices, nano-plasmonics, quantum electrodynamics, scanning tunnelling microscopy, and more. This rapidly expanding intersection of nanotechnology and quantum science/technology is mutually beneficial to both fields, laying claim to some of the most exciting scientific leaps of the last decade, with more on the horizon.

Scanned Single-Electron Probe inside a Silicon Electronic Device.

Solid-state devices can be fabricated at the atomic scale, with applications ranging from classical logic to current standards and quantum technologies. Although it is very desirable to probe these devices and the quantum states they host at the atomic scale, typical methods rely on long-ranged capacitive interactions, making this difficult. Here, we probe a silicon electronic device at the atomic scale using a localized electronic quantum dot induced directly within the device at a desired location, using the biased tip of a low-temperature scanning tunneling microscope. We demonstrate control over short-ranged tunnel coupling interactions of the quantum dot with the device's source reservoir using sub-nanometer position control of the tip and the quantum dot energy level using a voltage applied to the device's gate reservoir. Despite the ∼1 nm proximity of the quantum dot to the metallic tip, we find that the gate provides sufficient capacitance to enable a high degree of electric control. Combined with atomic-scale imaging, we use the quantum dot to probe applied electric fields and charge in individual defects in the device. This capability is expected to aid in the understanding of atomic-scale devices and the quantum states realized in them.

Readout and control of the spin-orbit states of two coupled acceptor atoms in a silicon transistor.

Coupling spin qubits to electric fields is attractive to simplify qubit manipulation and couple qubits over long distances. Electron spins in silicon offer long lifetimes, but their weak spin-orbit interaction makes electrical coupling challenging. Hole spins bound to acceptor dopants, spin-orbit-coupled J = 3/2 systems similar to Si vacancies in SiC and single Co dopants, are an electrically active spin system in silicon. However, J = 3/2 systems are much less studied than S = 1/2 electrons, and spin readout has not yet been demonstrated for acceptors in silicon. Here, we study acceptor hole spin dynamics by dispersive readout of single-hole tunneling between two coupled acceptors in a nanowire transistor. We identify m J = ±1/2 and m J = ±3/2 levels, and we use a magnetic field to overcome the initial heavy-light hole splitting and to tune the J = 3/2 energy spectrum. We find regimes of spin-like (+3/2 to -3/2) and charge-like (±1/2 to ±3/2) relaxations, separated by a regime of enhanced relaxation induced by mixing of light and heavy holes. The demonstrated control over the energy level ordering and hybridization are new tools in the J = 3/2 system that are crucial to optimize single-atom spin lifetime and electrical coupling.

Towards visualisation of central-cell-effects in scanning tunnelling microscope images of subsurface dopant qubits in silicon.

Atomic-scale understanding of phosphorus donor wave functions underpins the design and optimisation of silicon based quantum devices. The accuracy of large-scale theoretical methods to compute donor wave functions is dependent on descriptions of central-cell corrections, which are empirically fitted to match experimental binding energies, or other quantities associated with the global properties of the wave function. Direct approaches to understanding such effects in donor wave functions are of great interest. Here, we apply a comprehensive atomistic theoretical framework to compute scanning tunnelling microscopy (STM) images of subsurface donor wave functions with two central-cell correction formalisms previously employed in the literature. The comparison between central-cell models based on real-space image features and the Fourier transform profiles indicates that the central-cell effects are visible in the simulated STM images up to ten monolayers below the silicon surface. Our study motivates a future experimental investigation of the central-cell effects via the STM imaging technique with potential of fine tuning theoretical models, which could play a vital role in the design of donor-based quantum systems in scalable quantum computer architectures.

Charge-Insensitive Single-Atom Spin-Orbit Qubit in Silicon.

High fidelity entanglement of an on-chip array of spin qubits poses many challenges. Spin-orbit coupling (SOC) can ease some of these challenges by enabling long-ranged entanglement via electric dipole-dipole interactions, microwave photons, or phonons. However, SOC exposes conventional spin qubits to decoherence from electrical noise. Here, we propose an acceptor-based spin-orbit qubit in silicon offering long-range entanglement at a sweet spot where the qubit is protected from electrical noise. The qubit relies on quadrupolar SOC with the interface and gate potentials. As required for surface codes, 10^{5} electrically mediated single-qubit and 10^{4} dipole-dipole mediated two-qubit gates are possible in the predicted spin lifetime. Moreover, circuit quantum electrodynamics with single spins is feasible, including dispersive readout, cavity-mediated entanglement, and spin-photon entanglement. An industrially relevant silicon-based platform is employed.

Quantum computing with acceptor spins in silicon.

The states of a boron acceptor near a Si/SiO2 interface, which bind two low-energy Kramers pairs, have exceptional properties for encoding quantum information and, with the aid of strain, both heavy hole and light hole-based spin qubits can be designed. Whereas a light-hole spin qubit was introduced recently (arXiv:1508.04259), here we present analytical and numerical results proving that a heavy-hole spin qubit can be reliably initialised, rotated and entangled by electrical means alone. This is due to strong Rashba-like spin-orbit interaction terms enabled by the interface inversion asymmetry. Single qubit rotations rely on electric-dipole spin resonance (EDSR), which is strongly enhanced by interface-induced spin-orbit terms. Entanglement can be accomplished by Coulomb exchange, coupling to a resonator, or spin-orbit induced dipole-dipole interactions. By analysing the qubit sensitivity to charge noise, we demonstrate that interface-induced spin-orbit terms are responsible for sweet spots in the dephasing time [Formula: see text] as a function of the top gate electric field, which are close to maxima in the EDSR strength, where the EDSR gate has high fidelity. We show that both qubits can be described using the same starting Hamiltonian, and by comparing their properties we show that the complex interplay of bulk and interface-induced spin-orbit terms allows a high degree of electrical control and makes acceptors potential candidates for scalable quantum computation in Si.

Donor hyperfine Stark shift and the role of central-cell corrections in tight-binding theory.

Atomistic tight-binding (TB) simulations are performed to calculate the Stark shift of the hyperfine coupling for a single arsenic (As) donor in silicon (Si). The role of the central-cell correction is studied by implementing both the static and the non-static dielectric screenings of the donor potential, and by including the effect of the lattice strain close to the donor site. The dielectric screening of the donor potential tunes the value of the quadratic Stark shift parameter (η2) from -1.3 × 10(-3) µm(2) V(-2) for the static dielectric screening to -1.72 × 10(-3) µm(2) V(-2) for the non-static dielectric screening. The effect of lattice strain, implemented by a 3.2% change in the As-Si nearest-neighbour bond length, further shifts the value of η2 to -1.87 × 10(-3) µm(2) V(-2), resulting in an excellent agreement of theory with the experimentally measured value of -1.9 ± 0.2 × 10(-3) µm(2) V(-2). Based on our direct comparison of the calculations with the experiment, we conclude that the previously ignored non-static dielectric screening of the donor potential and the lattice strain significantly influence the donor wave function charge density and thereby leads to a better agreement with the available experimental data sets.

Probing the spin states of a single acceptor atom.

We demonstrate a single-hole transistor using an individual acceptor dopant embedded in a silicon channel. Magneto-transport spectroscopy reveals that the ground state splits as a function of magnetic field into four states, which is unique for a single hole bound to an acceptor in a bulk semiconductor. The two lowest spin states are heavy (|m(j)| = 3/2) and light (|m(j)| = 1/2) hole-like, a two-level system that can be electrically driven and is characterized by a magnetic field dependent and long relaxation time, which are properties of interest for qubits. Although the bulklike spin splitting of a boron atom is preserved in our nanotransistor, the measured Landé g-factors, |g(hh)| = 0.81 ± 0.06 and |g(lh)| = 0.85 ± 0.21 for heavy and light holes respectively, are lower than the bulk value.

Electrical characteristics and photocurrent spectral response of Si nanowires p-i-n junctions.

P-i-n junctions were fabricated along Si nanowires (SiNWs) via the conventional top-down approach using optical lithography. Each device comprises 500 identical SiNWs connected in parallel, and each SiNW has triangular cross-section with dimensions of ~6 nm (base) by ~8 nm (height). The photodiodes exhibit very good rectifying electrical characteristics with a low reverse bias current of ~0.2 fA per SiNW. The photocurrent spectral response exhibits three peaks between 400 nm to 700 nm, which arise due to local optical field enhancement associated with diffraction by the periodic SiNW array and interference in an air/SiO2/Si cavity.

Probing the gate--voltage-dependent surface potential of individual InAs nanowires using random telegraph signals.

We report a novel method for probing the gate-voltage dependence of the surface potential of individual semiconductor nanowires. The statistics of electronic occupation of a single defect on the surface of the nanowire, determined from a random telegraph signal, is used as a measure for the local potential. The method is demonstrated for the case of one or two switching defects in indium arsenide (InAs) nanowire field effect transistors at temperatures T=25-77 K. Comparison with a self-consistent model shows that surface potential variation is retarded in the conducting regime due to screening by surface states with density Dss≈10(12) cm(-2) eV(-1). Temperature-dependent dynamics of electron capture and emission producing the random telegraph signals are also analyzed, and multiphonon emission is identified as the process responsible for capture and emission of electrons from the surface traps. Two defects studied in detail had capture activation energies of EB≈50 meV and EB≈110 meV and cross sections of σ∞≈3×10(-19) cm2 and σ∞≈2×10(-17) cm2, respectively. A lattice relaxation energy of Sℏω=187±15 meV was found for the first defect.