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.
Comparative analyses of survival senescence by using life tables have identified generalizations including the observation that mammals senesce faster than similar-sized birds. These generalizations have been challenged because of limitations of life-table approaches and the growing appreciation that senescence is more than an increasing probability of death. Without using life tables, we examine senescence rates in annual individual fitness using 20 individual-based data sets of terrestrial vertebrates with contrasting life histories and body size. We find that senescence is widespread in the wild and equally likely to occur in survival and reproduction. Additionally, mammals senesce faster than birds because they have a faster life history for a given body size. By allowing us to disentangle the effects of two major fitness components our methods allow an assessment of the robustness of the prevalent life-table approach. Focusing on one aspect of life history - survival or recruitment - can provide reliable information on overall senescence.
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.
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). However, a powerful method applied to trapped ions in the context of atomic clocks is the use of particular spin transitions that are inherently robust to external perturbations. Here, we show that such 'clock transitions' can be observed for electron spins in the solid state, in particular using bismuth donors in silicon. This leads to dramatic enhancements in the electron spin coherence time, exceeding seconds. We find that electron spin qubits based on clock transitions become less sensitive to the local magnetic environment, including the presence of (29)Si nuclear spins as found in natural silicon. We expect the use of such clock transitions will be of additional significance for donor spins in nanodevices, mitigating the effects of magnetic or electric field noise arising from nearby interfaces and gates.
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. 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 (31)P in the purest available sample of (28)Si, at concentrations inaccessible to conventional measurements, measuring a solid-state coherence time of over 180 seconds.
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