High-fidelity spin qubit operation and algorithmic initialization above 1 K.

The encoding of qubits in semiconductor spin carriers has been recognized as a promising approach to a commercial quantum computer that can be lithographically produced and integrated at scale. However, the operation of the large number of qubits required for advantageous quantum applications will produce a thermal load exceeding the available cooling power of cryostats at millikelvin temperatures. As the scale-up accelerates, it becomes imperative to establish fault-tolerant operation above 1 K, at which the cooling power is orders of magnitude higher.

Waveguide-integrated silicon T centres.

The performance of modular, networked quantum technologies will be strongly dependent upon the quality of their quantum light-matter interconnects. Solid-state colour centres, and in particular T centres in silicon, offer competitive technological and commercial advantages as the basis for quantum networking technologies and distributed quantum computing. These newly rediscovered silicon defects offer direct telecommunications-band photonic emission, long-lived electron and nuclear spin qubits, and proven native integration into industry-standard, CMOS-compatible, silicon-on-insulator (SOI) photonic chips at scale.

On-demand electrical control of spin qubits.

Once called a 'classically non-describable two-valuedness' by Pauli, the electron spin forms a qubit that is naturally robust to electric fluctuations. Paradoxically, a common control strategy is the integration of micromagnets to enhance the coupling between spins and electric fields, which, in turn, hampers noise immunity and adds architectural complexity. Here we exploit a switchable interaction between spins and orbital motion of electrons in silicon quantum dots, without a micromagnet.

Optical observation of single spins in silicon.

The global quantum internet will require long-lived, telecommunications-band photon-matter interfaces manufactured at scale. Preliminary quantum networks based on photon-matter interfaces that meet a subset of these demands are encouraging efforts to identify new high-performance alternatives. Silicon is an ideal host for commercial-scale solid-state quantum technologies.

Linear Hyperfine Tuning of Donor Spins in Silicon Using Hydrostatic Strain.

We experimentally study the coupling of group V donor spins in silicon to mechanical strain, and measure strain-induced frequency shifts that are linear in strain, in contrast to the quadratic dependence predicted by the valley repopulation model (VRM), and therefore orders of magnitude greater than that predicted by the VRM for small strains |ϵ|<10^{-5}. Through both tight-binding and first principles calculations we find that these shifts arise from a linear tuning of the donor hyperfine interaction term by the hydrostatic component of strain and achieve semiquantitative agreement with the experimental values. Our results provide a framework for making quantitative predictions of donor spins in silicon nanostructures, such as those being used to develop silicon-based quantum processors and memories.

A photonic platform for donor spin qubits in silicon.

Donor spins in silicon are highly competitive qubits for upcoming quantum technologies, offering complementary metal-oxide semiconductor compatibility, coherence () times of minutes to hours, and simultaneous initialization, manipulation, and readout fidelities near ~99.9%. This allows for many quantum error correction protocols, which will be essential for scale-up.

Reaching the quantum limit of sensitivity in electron spin resonance.

The detection and characterization of paramagnetic species by electron spin resonance (ESR) spectroscopy is widely used throughout chemistry, biology and materials science, from in vivo imaging to distance measurements in spin-labelled proteins. ESR relies on the inductive detection of microwave signals emitted by the spins into a coupled microwave resonator during their Larmor precession. However, such signals can be very small, prohibiting the application of ESR at the nanoscale (for example, at the single-cell level or on individual nanoparticles).

Optical pumping and readout of bismuth hyperfine states in silicon for atomic clock applications.

The push for a semiconductor-based quantum information technology has renewed interest in the spin states and optical transitions of shallow donors in silicon, including the donor bound exciton transitions in the near-infrared and the Rydberg, or hydrogenic, transitions in the mid-infrared. The deepest group V donor in silicon, bismuth, has a large zero-field ground state hyperfine splitting, comparable to that of rubidium, upon which the now-ubiquitous rubidium atomic clock time standard is based. Here we show that the ground state hyperfine populations of bismuth can be read out using the mid-infrared Rydberg transitions, analogous to the optical readout of the rubidium ground state populations upon which rubidium clock technology is based.

Hybrid optical-electrical detection of donor electron spins with bound excitons in silicon.

Electrical detection of spins is an essential tool for understanding the dynamics of spins, with applications ranging from optoelectronics and spintronics, to quantum information processing. For electron spins bound to 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 donor electron spin resonance in an ensemble by transport through a silicon device, using optically driven donor-bound exciton transitions.

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.

Conditional control of donor nuclear spins in silicon using stark shifts.

Electric fields can be used to tune donor spins in silicon using the Stark shift, whereby the donor electron wave function is displaced by an electric field, modifying the hyperfine coupling between the electron spin and the donor nuclear spin. We present a technique based on dynamic decoupling of the electron spin to accurately determine the Stark shift, and illustrate this using antimony donors in isotopically purified silicon-28. We then demonstrate two different methods to use a dc electric field combined with an applied resonant radio-frequency (rf) field to conditionally control donor nuclear spins.

Room-temperature quantum bit storage exceeding 39 minutes using ionized donors in silicon-28.

Quantum memories capable of storing and retrieving coherent information for extended times at room temperature would enable a host of new technologies. Electron and nuclear spin qubits using shallow neutral donors in semiconductors have been studied extensively but are limited to low temperatures (≲10 kelvin); however, the nuclear spins of ionized donors have the potential for high-temperature operation. We used optical methods and dynamical decoupling to realize this potential for an ensemble of phosphorous-31 donors in isotopically purified silicon-28 and observed a room-temperature coherence time of over 39 minutes.

Atomic clock transitions in silicon-based spin qubits.

A major challenge in using spins in the solid state for quantum technologies is protecting them from sources of decoherence. This is particularly important in nanodevices where the proximity of material interfaces, and their associated defects, can play a limiting role. Spin decoherence can be addressed to varying degrees by improving material purity or isotopic composition, for example, or active error correction methods such as dynamic decoupling (or even combinations of the two).

Quantum information storage for over 180 s using donor spins in a 28Si "semiconductor vacuum".

A quantum computer requires systems that are isolated from their environment, but can be integrated into devices, and whose states can be measured with high accuracy. Nuclear spins in solids promise long coherence lifetimes, but they are difficult to initialize into known states and to detect with high sensitivity. We show how the distinctive optical properties of enriched (28)Si enable the use of hyperfine-resolved optical transitions, as previously applied to great effect for isolated atoms and ions in vacuum.

Violation of a Leggett-Garg inequality with ideal non-invasive measurements.

The quantum superposition principle states that an entity can exist in two different states simultaneously, counter to our 'classical' intuition. Is it possible to understand a given system's behaviour without such a concept? A test designed by Leggett and Garg can rule out this possibility. The test, originally intended for macroscopic objects, has been implemented in various systems.

Electron spin coherence exceeding seconds in high-purity silicon.

Silicon is one of the most promising semiconductor materials for spin-based information processing devices. Its advanced fabrication technology facilitates the transition from individual devices to large-scale processors, and the availability of a (28)Si form with no magnetic nuclei overcomes a primary source of spin decoherence in many other materials. Nevertheless, the coherence lifetimes of electron spins in the solid state have typically remained several orders of magnitude lower than that achieved in isolated high-vacuum systems such as trapped ions.

Entanglement in a solid-state spin ensemble.

Entanglement is the quintessential quantum phenomenon. It is a necessary ingredient in most emerging quantum technologies, including quantum repeaters, quantum information processing and the strongest forms of quantum cryptography. Spin ensembles, such as those used in liquid-state nuclear magnetic resonance, have been important for the development of quantum control methods.

Electron spin coherence and electron nuclear double resonance of Bi donors in natural Si.

Donors in silicon hold considerable promise for emerging quantum technologies, due to their uniquely long electron spin coherence times. Bismuth donors in silicon differ from more widely studied group V donors, such as phosphorous, in several significant respects: They have the strongest binding energy (70.98 meV), a large nuclear spin (I=9/2), and a strong hyperfine coupling constant (A=1475.

Hyperfine structure and nuclear hyperpolarization observed in the bound exciton luminescence of Bi donors in natural Si.

As the deepest group-V donor in Si, Bi has by far the largest hyperfine interaction and also a large I = 9/2 nuclear spin. At zero field this splits the donor ground state into states having total spin 5 and 4, which are fully resolved in the photoluminescence spectrum of Bi donor bound excitons. Under a magnetic field, the 60 expected allowed transitions cannot be individually resolved, but the effects of the nuclear spin distribution, -9/2 < or = I(z) < or = 9/2, are clearly observed.

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.

Reduction of the linewidths of deep luminescence centers in 28Si reveals fingerprints of the isotope constituents.

Dramatic reductions of the linewidths of well-known deep centers in 28Si reveal "isotopic fingerprints" of the constituents. The approximately 1014 meV Cu center, thought to be either a Cu pair or an isolated Cu, is shown to contain four Cu atoms, and the approximately 780 meV Ag center is shown to contain four Ag. The approximately 944 meV ;{*}Cu center, thought to be a different configuration of a Cu pair, in fact contains three Cu and one Ag, and a new two-Cu two-Ag center is found.

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.

Temperature dependence of the energy gap of semiconductors in the low-temperature limit.

The temperature dependence of the electronic states and energy gaps of semiconductors is an old but still important experimental and theoretical topic. Remarkably, extant results do not clarify the asymptotic T-->0 behavior. Recent breakthroughs in the spectroscopy of enriched 28Si allow us to measure changes in the band gap over the liquid 4He temperature range with an astounding precision of one part in 10(8), revealing a T4.

Impurity absorption spectroscopy in 28Si: the importance of inhomogeneous isotope broadening.

We report high-resolution infrared absorption spectra of the neutral donors phosphorus and lithium, and the neutral acceptor boron, in isotopically pure 28Si crystals. Surprisingly, many of the transitions are much sharper than previously reported in natural Si. In particular, the 2p(0) line of phosphorus in 28Si has a full width at half maximum of only 4.

Origin of the residual acceptor ground-state splitting in silicon.

The residual ground-state splitting of acceptors in high-quality silicon has been studied intensely by different experimental techniques for several decades. Recently, photoluminescence studies of isotopically pure silicon revealed the ground-state splitting to result from the random distribution of isotopes in natural silicon. Here we present a new model that explains these surprising experimental results, and discuss the implications for acceptor ground-state splittings observed in other isotopically mixed semiconductors, as well as for the acceptor ground state in semiconductor alloys.