H. Riemann

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. Here we examine electron spin coherence of donors in pure (28)Si material (residual (29)Si concentration <50 ppm) with donor densities of 10(14)-10(15) cm(-3). We elucidate three mechanisms for spin decoherence, active at different temperatures, and extract a coherence lifetime T(2) up to 2 s. In this regime, we find the electron spin is sensitive to interactions with other donor electron spins separated by ~200 nm. A magnetic field gradient suppresses such interactions, producing an extrapolated electron spin T(2) of 10 s at 1.8 K. These coherence lifetimes are without peer in the solid state and comparable to high-vacuum qubits, making electron spins of donors in silicon ideal components of quantum computers, or quantum memories for systems such as superconducting qubits.

Room-Temperature Quantum Bit Storage Exceeding 39 Minutes Using Ionized Donors in Silicon-28

Long-Lived Donors Quantum computing in materials such as silicon would simplify integration with existing electronic components; however, the coherence times of such qubits, especially at room temperature, are affected by the interaction with the busy environment of a solid. Eliminating isotopic impurities from the host material improves coherence times, as observed for qubits, based on the nuclear spin of neutral P donors in Si. Saeedi et al. (p. 830) modified this system by using charged P donors instead of neutral ones; by manipulating the states of the donors optically and using dynamical decoupling, the coherence time of the qubits was extended to 3 hours at cryogenic temperatures and 39 minutes at room temperature. Isotopically purified silicon is used to extend the coherence time of qubits based on phosphorus impurities. 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. We further showed that a coherent spin superposition can be cycled from 4.2 kelvin to room temperature and back, and we report a cryogenic coherence time of 3 hours in the same system.

Quantum information storage for over 180 s using donor spins in a 28si “semiconductor vacuum”

Extending Quantum Memory Practical applications in quantum communication and quantum computation require the building blocks—quantum bits and quantum memory—to be sufficiently robust and long-lived to allow for manipulation and storage (see the Perspective by Boehme and McCarney). Steger et al. (p. 1280) demonstrate that the nuclear spins of 31P impurities in an almost isotopically pure sample of 28Si can have a coherence time of as long as 192 seconds at a temperature of ∼1.7 K. In diamond at room temperature, Maurer et al. (p. 1283) show that a spin-based qubit system comprised of an isotopic impurity (13C) in the vicinity of a color defect (a nitrogen-vacancy center) could be manipulated to have a coherence time exceeding one second. Such lifetimes promise to make spin-based architectures feasible building blocks for quantum information science. An almost isotopically pure sample of 28Si provides a vacuumlike environment for 31P qubits. 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 28Si enable the use of hyperfine-resolved optical transitions, as previously applied to great effect for isolated atoms and ions in vacuum. Together with efficient Auger photoionization, these resolved hyperfine transitions permit rapid nuclear hyperpolarization and electrical spin-readout. We combine these techniques to detect nuclear magnetic resonance from dilute 31P in the purest available sample of 28Si, at concentrations inaccessible to conventional measurements, measuring a solid-state coherence time of over 180 seconds.

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. However, these demonstrations contain no entanglement and ultimately constitute classical simulations of quantum algorithms. Here we report the on-demand generation of entanglement between an ensemble of electron and nuclear spins in isotopically engineered, phosphorus-doped silicon. We combined high-field (3.4 T), low-temperature (2.9 K) electron spin resonance with hyperpolarization of the 31P nuclear spin to obtain an initial state of sufficient purity to create a non-classical, inseparable state. The state was verified using density matrix tomography based on geometric phase gates, and had a fidelity of 98% relative to the ideal state at this field and temperature. The entanglement operation was performed simultaneously, with high fidelity, on 1010 spin pairs; this fulfils one of the essential requirements for a silicon-based quantum information processor.

The Avogadro Constant Determination via Enriched Silicon-28

This review describes the efforts of several national metrology institutes to replace the present definition of the kilogram by a new one based on the mass of a given number of 12C atoms. This requires the determination of the Avogadro constant with a relative uncertainty no greater than 2 ? 10?8. Since in previous attempts the most significant limiting factor has been the measurement of the average molar mass of the natural silicon, an international collaboration has been set up to produce a 5 kg single crystal with an isotope enrichment over 99.985%. The technological steps enabling the production of this high-purity 28Si crystal are also reported.

High Purity Isotopically Enriched 29Si and 30Si Single Crystals: Isotope Separation, Purification, and Growth

We report the successful isotope separation and bulk single crystal growth of 29Si and 30Si stable isotopes. The isotopic enrichments of the 29Si and 30Si single crystals determined by mass spectrometry are 99.23% and 99.74%, respectively. Both crystals have the electrically active net-impurity concentration less than 1015 cm-3. Thanks to the result of this work and the 28Si crystals we grew previously, high quality single crystals of every stable Si isotope (28Si, 29Si, and 30Si) have been made available for a wide variety of basic research and industrial applications.

Far-infrared stimulated emission from optically excited bismuth donors in silicon

Far-infrared stimulated emission from optically pumped neutral Bi donors in silicon has been obtained. Lasing with wavelengths of 52.2 and 48.6 μm from the intra-center 2p±→1s(E:Γ8),1s(T2:Γ8) transitions has been realized under CO2 laser pumping. The population inversion mechanism is based on fast optical-phonon-assisted relaxation from the 2p0 and 2s excited states directly to the ground 1s(A) state leading to relatively small population in the intermediate 1s(E), 1s(T2) excited states.

Interface shape, heat transfer and fluid flow in the floating zone growth of large silicon crystals with the needle-eye technique

A computer simulation is carried out to study the interface shape, heat transfer and fluid flow in the floating zone (FZ) growth of large (> 100 mm) Si crystals with the needle-eye technique and with feed/crystal rotation. Natural convection, thermocapillary convection, electromagnetic (EM) forces and rotation in the melt are considered. The unknown shape of the molten zone is calculated as a coupled thermal-electromagnetic-hydrodynamic problem and compared with that observed during experiments. The effects of the growth rate and the process stage on the shape of the interface are demonstrated. It was observed that natural convection and rotation dominate over thermocapillary and EM convection, at least for conditions corresponding to the industrial FZ Si production with the needle-eye technique. It is shown that under these conditions the rotation destabilizes the flow and only unsteady flows exist in the molten zone. The calculated distributions of the oscillation amplitude of the tangential velocity at the growing interface correspond to the radial resistivity distributions measured in the single crystal by the photo-scanning method.

Stimulated terahertz emission from group-V donors in silicon under intracenter photoexcitation

Frequency-tunable radiation from the free electron laser FELIX was used to excite neutral phosphorus and bismuth donors embedded in bulk monocrystalline silicon. Lasing at terahertz frequencies has been observed at liquid helium temperature while resonant pumping of odd parity impurity states. The threshold was about two orders of magnitude below the value for photoionization pumping. The influence of nonequilibrium intervalley TO phonons on the population of excited Bi impurity states is discussed.

Stimulated terahertz emission from arsenic donors in silicon

Stimulated emission has been obtained from intra-center donor transitions in silicon monocrystals doped by arsenic. The Si:As laser was optically excited by radiation from a CO2 laser. The emission spectrum consists of two lines corresponding to the 2p±→1s(E) and 2p±→1s(T2) intra-center arcenic transitions. The population inversion is formed due to fast 2s→1s(A1) electron relaxation assisted by intervalley longitudinal acoustic f-phonon emission. This keeps the excited donor states below the 2p± state unpopulated. Thus population inversion occurs between the 2p± state and the 1s(E), 1s(T2) states.