Coherent spin qubit transport in silicon

A fault-tolerant quantum processor may be configured using stationary qubits interacting only with their nearest neighbours, but at the cost of significant overheads in physical qubits per logical qubit. Such overheads could be reduced by coherently transporting qubits across the chip, allowing connectivity beyond immediate neighbours. Here we demonstrate high-fidelity coherent transport of an electron spin qubit between quantum dots in isotopically-enriched silicon. We observe qubit precession in the inter-site tunnelling regime and assess the impact of qubit transport using Ramsey interferometry and quantum state tomography techniques. We report a polarization transfer fidelity of 99.97% and an average coherent transfer fidelity of 99.4%. Our results provide key elements for high-fidelity, on-chip quantum information distribution, as long envisaged, reinforcing the scaling prospects of silicon-based spin qubits.

Coherent spin control of s-, p-, d- and f-electrons in a silicon quantum dot

Once the periodic properties of elements were unveiled, chemical behaviour could be understood in terms of the valence of atoms. Ideally, this rationale would extend to quantum dots, and quantum computation could be performed by merely controlling the outer-shell electrons of dot-based qubits. Imperfections in semiconductor materials disrupt this analogy, so real devices seldom display a systematic many-electron arrangement. We demonstrate here an electrostatically confined quantum dot that reveals a well defined shell structure. We observe four shells (31 electrons) with multiplicities given by spin and valley degrees of freedom. Various fillings containing a single valence electron-namely 1, 5, 13 and 25 electrons-are found to be potential qubits. An integrated micromagnet allows us to perform electrically-driven spin resonance (EDSR), leading to faster Rabi rotations and higher fidelity single qubit gates at higher shell states. We investigate the impact of orbital excitations on single qubits as a function of the dot deformation and exploit it for faster qubit control.

Single-spin qubits in isotopically enriched silicon at low magnetic field

Single-electron spin qubits employ magnetic fields on the order of 1 Tesla or above to enable quantum state readout via spin-dependent-tunnelling. This requires demanding microwave engineering for coherent spin resonance control, which limits the prospects for large scale multi-qubit systems. Alternatively, singlet-triplet readout enables high-fidelity spin-state measurements in much lower magnetic fields, without the need for reservoirs. Here, we demonstrate low-field operation of metal-oxide-silicon quantum dot qubits by combining coherent single-spin control with high-fidelity, single-shot, Pauli-spin-blockade-based ST readout. We discover that the qubits decohere faster at low magnetic fields with [Formula: see text] μs and [Formula: see text] μs at 150 mT. Their coherence is limited by spin flips of residual 29Si nuclei in the isotopically enriched 28Si host material, which occur more frequently at lower fields. Our finding indicates that new trade-offs will be required to ensure the frequency stabilization of spin qubits, and highlights the importance of isotopic enrichment of device substrates for the realization of a scalable silicon-based quantum processor.

Three-dimensional localization spectroscopy of individual nuclear spins with sub-Angstrom resolution

Nuclear magnetic resonance (NMR) spectroscopy is a powerful method for analyzing the chemical composition and molecular structure of materials. At the nanometer scale, NMR has the prospect of mapping the atomic-scale structure of individual molecules, provided a method that can sensitively detect single nuclei and measure inter-atomic distances. Here, we report on precise localization spectroscopy experiments of individual 13C nuclear spins near the central electronic sensor spin of a nitrogen-vacancy (NV) center in a diamond chip. By detecting the nuclear free precession signals in rapidly switchable external magnetic fields, we retrieve the three-dimensional spatial coordinates of the nuclear spins with sub-Angstrom resolution and for distances beyond 10 Å. We further show that the Fermi contact contribution can be constrained by measuring the nuclear g-factor enhancement. The presented method will be useful for mapping atomic positions in single molecules, an ambitious yet important goal of nanoscale nuclear magnetic resonance spectroscopy.

Fabrication of arrays of tapered silicon micro-/nano-pillars by metal-assisted chemical etching and anisotropic wet etching

Fabrication of a 2D square lattice array of intentionally tapered micro-/nano-silicon pillars by metal-assisted chemical etching (MACE) of silicon wafers is reported. The pillars are square rod shaped with the cross-sections in the range 0.2 × 0.2-0.9 × 0.9 μm² and heights 3-7 μm. The spacing between pillars in the 2D square lattice was controlled between 0.5 and 3.0 μm. While the pillars after MACE had the high aspect ratio ∼1:5, subsequent anisotropic wet etching in potassium hydroxide solution led to 80°-89.5° tapers with smooth sidewalls. The resulting taper angle showed the relation with geometry of pillar structures; the spacing 0.5-3.0 μm led to the tapering angle 89.5°-80° for 3 and 5 μm tall pillars but 7 μm tall pillars showed no dependency between the tapering angle and the inter-pillar spacing. Such an array of silicon tapered-rods with smooth sidewalls is expected to be applicable as a mold in nanoimprinting applications.

High-Resolution Quantum Sensing with Shaped Control Pulses

We investigate the application of amplitude-shaped control pulses for enhancing the time and frequency resolution of multipulse quantum sensing sequences. Using the electronic spin of a single nitrogen-vacancy center in diamond and up to 10 000 coherent microwave pulses with a cosine square envelope, we demonstrate 0.6-ps timing resolution for the interpulse delay. This represents a refinement by over 3 orders of magnitude compared to the 2-ns hardware sampling. We apply the method for the detection of external ac magnetic fields and nuclear magnetic resonance signals of ^{13}C spins with high spectral resolution. Our method is simple to implement and especially useful for quantum applications that require fast phase gates, many control pulses, and high fidelity.

Quadrupole shift of nuclear magnetic resonance of donors in silicon at low magnetic field

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.

Electron Spin Coherence of Shallow Donors in Natural and Isotopically Enriched Germanium

Germanium is a widely used material for electronic and optoelectronic devices and recently it has become an important material for spintronics and quantum computing applications. Donor spins in silicon have been shown to support very long coherence times (T_{2}) when the host material is isotopically enriched to remove any magnetic nuclei. Germanium also has nonmagnetic isotopes so it is expected to support long T_{2}'s while offering some new properties. Compared to Si, Ge has a strong spin-orbit coupling, large electron wave function, high mobility, and highly anisotropic conduction band valleys which will all give rise to new physics. In this Letter, the first pulsed electron spin resonance measurements of T_{2} and the spin-lattice relaxation (T_{1}) times for ^{75}As and ^{31}P donors in natural and isotopically enriched germanium are presented. We compare samples with various levels of isotopic enrichment and find that spectral diffusion due to ^{73}Ge nuclear spins limits the coherence in samples with significant amounts of ^{73}Ge. For the most highly enriched samples, we find that T_{1} limits T_{2} to T_{2}=2T_{1}. We report an anisotropy in T_{1} and the ensemble linewidths for magnetic fields oriented along different crystal axes but do not resolve any angular dependence to the spectral-diffusion-limited T_{2} in samples with ^{73}Ge.

Phonon Engineering in Isotopically Disordered Silicon Nanowires

The introduction of stable isotopes in the fabrication of semiconductor nanowires provides an additional degree of freedom to manipulate their basic properties, design an entirely new class of devices, and highlight subtle but important nanoscale and quantum phenomena. With this perspective, we report on phonon engineering in metal-catalyzed silicon nanowires with tailor-made isotopic compositions grown using isotopically enriched silane precursors (28)SiH4, (29)SiH4, and (30)SiH4 with purity better than 99.9%. More specifically, isotopically mixed nanowires (28)Si(x)(30)Si(1-x) with a composition close to the highest mass disorder (x ∼ 0.5) were investigated. The effect of mass disorder on the phonon behavior was elucidated and compared to that in isotopically pure (29)Si nanowires having a similar reduced mass. We found that the disorder-induced enhancement in phonon scattering in isotopically mixed nanowires is unexpectedly much more significant than in bulk crystals of close isotopic compositions. This effect is explained by a nonuniform distribution of (28)Si and (30)Si isotopes in the grown isotopically mixed nanowires with local compositions ranging from x = ∼0.25 to 0.70. Moreover, we also observed that upon heating, phonons in (28)Si(x)(30)Si(1-x) nanowires behave remarkably differently from those in (29)Si nanowires suggesting a reduced thermal conductivity induced by mass disorder. Using Raman nanothermometry, we found that the thermal conductivity of isotopically mixed (28)Si(x)(30)Si(1-x) nanowires is ∼30% lower than that of isotopically pure (29)Si nanowires in agreement with theoretical predictions.

Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking

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 of donor-based quantum computing in silicon. By studying the influence of the shape and power of the control pulses, we find evidence that the present limitation to the gate fidelity is mostly related to the external hardware and not the intrinsic behaviour of the qubit.

Spectroscopy of surface-induced noise using shallow spins in diamond

We report on the noise spectrum experienced by few nanometer deep nitrogen-vacancy centers in diamond as a function of depth, surface coating, magnetic field and temperature. Analysis reveals a double-Lorentzian noise spectrum consistent with a surface electronic spin bath in the low frequency regime, along with a faster noise source attributed to surface-modified phononic coupling. These results shed new light on the mechanisms responsible for surface noise affecting shallow spins at semiconductor interfaces, and suggests possible directions for further studies. We demonstrate dynamical decoupling from the surface noise, paving the way to applications ranging from nanoscale NMR to quantum networks.

Inductive measurement of optically hyperpolarized phosphorous donor nuclei in an isotopically enriched silicon-28 crystal

We experimentally demonstrate the first inductive readout of optically hyperpolarized phosphorus-31 donor nuclear spins in an isotopically enriched silicon-28 crystal. The concentration of phosphorus donors in the crystal was 1.5×10(15)  cm(-3), 3 orders of magnitude lower than has previously been detected via direct inductive detection. The signal-to-noise ratio measured in a single free induction decay from a 1  cm(3) sample (≈10(15) spins) was 113. By transferring the sample to an X-band ESR spectrometer, we were able to obtain a lower bound for the nuclear spin polarization at 1.7 K of ∼64%. The (31)P-T2 measured with a Hahn echo sequence was 420 ms at 1.7 K, which was extended to 1.2 s with a Carr Purcell cycle. The T1 of the (31)P nuclear spins at 1.7 K is extremely long and could not be determined, as no decay was observed even on a time scale of 4.5 h. Optical excitation was performed with a 1047 nm laser, which provided above-band-gap excitation of the silicon. The buildup of the hyperpolarization at 4.2 K followed a single exponential with a characteristic time of 577 s, while the buildup at 1.7 K showed biexponential behavior with characteristic time constants of 578 and 5670 s.

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.

Investigation of surface magnetic noise by shallow spins in diamond

We present measurements of spin relaxation times (T1, T1ρ, T2) on very shallow (≲5  nm) nitrogen-vacancy centers in high-purity diamond single crystals. We find a reduction of spin relaxation times up to 30 times compared to bulk values, indicating the presence of ubiquitous magnetic impurities associated with the surface. Our measurements yield a density of 0.01-0.1μB/nm2 and a characteristic correlation time of 0.28(3) ns of surface states, with little variation between samples and chemical surface terminations. A low temperature measurement further confirms that fluctuations are thermally activated. The data support the atomistic picture where impurities are associated with the top carbon layers, and not with terminating surface atoms or adsorbate molecules. The low spin density implies that the presence of a single surface impurity is sufficient to cause spin relaxation of a shallow nitrogen-vacancy center.

Negatively charged nitrogen-vacancy centers in a 5 nm thin 12C diamond film

We report successful introduction of negatively charged nitrogen-vacancy (NV(-)) centers in a 5 nm thin, isotopically enriched ([(12)C] = 99.99%) diamond layer by CVD. The present method allows for the formation of NV(-) in such a thin layer even when the surface is terminated by hydrogen atoms. NV(-) centers are found to have spin coherence times of between T2 ~ 10-100 μs at room temperature. Changing the surface termination to oxygen or fluorine leads to a slight increase in the NV(-) density, but not to any significant change in T2. The minimum detectable magnetic field estimated by this T2 is 3 nT after 100 s of averaging, which would be sufficient for the detection of nuclear magnetic fields exerted by a single proton. We demonstrate the suitability for nanoscale NMR by measuring the fluctuating field from ~10(4) proton nuclei placed on top of the 5 nm diamond film.

Spin susceptibility of noncentrosymmetric heavy-fermion superconductor CeIrSi3 under pressure: 29Si Knight-shift study on single crystal

We report 29Si NMR study on a single crystal of the heavy-fermion superconductor CeIrSi3 without an inversion symmetry along the c axis. The 29Si Knight-shift measurements under pressure have revealed that the spin susceptibility for the ab plane decreases slightly below T(c), whereas along the c axis it does not change at all. The result can be accounted for by the spin susceptibility in the superconducting state being dominated by the strong antisymmetric (Rashba-type) spin-orbit interaction that originates from the absence of an inversion center along the c axis and it being much larger than superconducting condensation energy. This is the first observation which exhibits an anisotropy of the spin susceptibility below T(c) in the noncentrosymmetric superconductor dominated by strong Rashba-type spin-orbit interaction.

Simultaneous subsecond hyperpolarization of the nuclear and electron spins of phosphorus in silicon by optical pumping of exciton transitions

We demonstrate a method which can hyperpolarize both the electron and nuclear spins of 31P donors in Si at low field, where both would be essentially unpolarized in equilibrium. It is based on the selective ionization of donors in a specific hyperfine state by optically pumping donor bound exciton hyperfine transitions, which can be spectrally resolved in 28Si. Electron and nuclear polarizations of 90% and 76%, respectively, are obtained in less than a second, providing an initialization mechanism for qubits based on these spins, and enabling further ESR and NMR studies on dilute 31P in 28Si.

Optical detection and ionization of donors in specific electronic and nuclear spin States

We resolve the remarkably sharp bound exciton transitions of highly enriched 28Si using a single-frequency laser and photoluminescence excitation spectroscopy, as well as photocurrent spectroscopy. Well-resolved doublets in the spectrum of the 31P donor reflect the hyperfine coupling of the electronic and nuclear donor spins. The optical detection of the nuclear spin state, and selective pumping and ionization of donors in specific electronic and nuclear spin states, suggests a number of new possibilities which could be useful for the realization of silicon-based quantum computers.

Isotope dependence of the lifetime of the vibration of oxygen in silicon

By simply changing the isotopes of the Si atoms that neighbor an oxygen Oi atom in crystalline silicon, the measured decay rate tau of the asymmetric-stretch vibration (nu3=1136 cm-1) of oxygen (Oi) in silicon changes by a factor of approximately 2.5. These data establish that nu3 decays by creating one nu1 symmetric-stretch, local-vibrational mode of the Si-Oi-Si structure. If the residual energy (nu3-nu1) is less than the maximum frequency num of the host lattice, as for 28Si-16O-28Si in natural silicon, then it is emitted as one lattice mode, and tau depends on the density of one-phonon states at nu3-nu1. If (nu3-nu1)>num, as for 16O in single-isotope 30Si silicon, two lattice modes are created in addition to nu1, increasing tau. Prediction of tau for a particular defect clearly requires a detailed knowledge of that defect.

Mechanism of superconductivity in the polyhedral-network compound Ba8Si46

The silicon clathrates--materials composed of metal-doped Si(20) dodecahedra--were identified as the first superconductors based on pure silicon networks. The mechanism of superconductivity in these materials can be obtained by studying their phonon modes, as modified by isotope substitution, and specific-heat measurements. Here, we present experimental studies that provide strong evidence that superconductivity in Ba(8)Si(46) is explained in the framework of phonon-mediated Bardeen-Cooper-Schriefer theory. Analyses using the McMillan approximation of the Eliashberg equation indicate that the superconducting mechanism is in the medium coupling regime, but at the high-end limit. The large density of states at the Fermi level, which arises from hybridization of the Si(20) cluster and Ba orbitals, is responsible for the unexpectedly high superconducting temperature. The temperature evolution of the specific heat unambiguously shows that this is an s-wave symmetry superconductor.

All-silicon quantum computer

A solid-state implementation of a quantum computer composed entirely of silicon is proposed. Qubits are 29Si nuclear spins arranged as chains in a 28Si (spin-0) matrix with Larmor frequencies separated by a large magnetic field gradient. No impurity dopants or electrical contacts are needed. Initialization is accomplished by optical pumping, algorithmic cooling, and pseudo-pure state techniques. Magnetic resonance force microscopy is used for ensemble measurement.