The decoherence of mixed electron-nuclear spin qubits is a topic of great current importance, but understanding is still lacking: while important decoherence mechanisms for spin qubits arise from quantum spin bath environments with slow decay of correlations, the only analytical framework for explaining observed sharp variations of decoherence times with magnetic field is based on the suppression of classical noise. Here we obtain a general expression for decoherence times of the central spin system which exposes significant differences between quantum-bath decoherence and decoherence by classical field noise. We perform measurements of decoherence times of bismuth donors in natural silicon using both electron spin resonance (ESR) and nuclear magnetic resonance (NMR) transitions, and in both cases find excellent agreement with our theory across a wide parameter range. The universality of our expression is also tested by quantitative comparisons with previous measurements of decoherence around 'optimal working points' or 'clock transitions' where decoherence is strongly suppressed. We further validate our results by comparison to cluster expansion simulations.

Pulsed magnetic resonance allows the quantum state of electronic and nuclear spins to be controlled on the timescale of nanoseconds and microseconds respectively. The time required to flip dilute spins is orders of magnitude shorter than their coherence times, leading to several schemes for quantum information processing with spin qubits. Instead, we investigate 'hybrid nuclear-electronic' qubits consisting of near 50:50 superpositions of the electronic and nuclear spin states. Using bismuth-doped silicon, we demonstrate quantum control over these states in 32 ns, which is orders of magnitude faster than previous experiments using pure nuclear states. The coherence times of up to 4 ms are five orders of magnitude longer than the manipulation times, and are limited only by naturally occurring (29)Si nuclear spin impurities. We find a quantitative agreement between our experiments and an analytical theory for the resonance positions, as well as their relative intensities and Rabi oscillation frequencies. These results bring spins in a solid material a step closer to research on ion-trap qubits.

Hybrid qubit systems combining electronic spins with nearby ("proximate") nuclear spin registers offer a promising avenue towards quantum information processing, with even multi-spin error correction protocols recently demonstrated in diamond. However, for the important platform offered by spins of donor atoms in cryogenically-cooled silicon, decoherence mechanisms of 29 Si proximate nuclear spins are not yet well understood. The reason is partly because proximate spins lie within a so-called "frozen core" region where the donor electronic hyperfine interaction strongly suppresses nuclear dynamics. We investigate the decoherence of a central proximate nuclear qubit arising from quantum spin baths outside, as well as inside, the frozen core around the donor electron. We consider the effect of a very large nuclear spin bath comprising many ( 10 8 ) weakly contributing pairs outside the frozen core. We also propose that there may be an important contribution from a few (of order 100) symmetrically sited nuclear spin pairs ("equivalent pairs"), which were not previously considered as their effect is negligible outside the frozen core. If equivalent pairs represent a measurable source of decoherence, nuclear coherence decays could provide sensitive probes of the symmetries of electronic wavefunctions. For the phosphorus donor system, we obtain T2n values of order 1 second for both the "far bath" and "equivalent pair" models, confirming the suitability of proximate nuclei in silicon as very long-lived spin qubits.

We present pulsed electron-nuclear double resonance (ENDOR) experiments which enable us to characterize the coupling between bismuth donor spin-qubits in Si and the surrounding spin-bath of 29 Si impurities which provides the dominant decoherence mechanism (nuclear spin diffusion) at low temperatures (< 16 K). Decoupling from the spin-bath is predicted and cluster correlation expansion simulations show near-complete suppression of spin diffusion, at optimal working points. The suppression takes the form of sharply peaked divergences of the spin diffusion coherence time, in contrast with previously identified broader regions of insensitivity to classical fluctuations. ENDOR data shows anisotropic contributions are comparatively weak, so the form of the divergences is independent of crystal orientation.

There are two distinct techniques of proven effectiveness for extending the coherence lifetime of spin qubits in environments of other spins. One is dynamical decoupling, whereby the qubit is subjected to a carefully timed sequence of control pulses; the other is tuning the qubit towards 'optimal working points' (OWPs), which are sweet-spots for reduced decoherence in magnetic fields. By means of quantum many-body calculations, we investigate the effects of dynamical decoupling pulse sequences far from and near OWPs for a central donor qubit subject to decoherence from a nuclear spin bath. Key to understanding the behavior is to analyse the degree of suppression of the usually dominant contribution from independent pairs of flip-flopping spins within the many-body quantum bath. We find that to simulate recently measured Hahn echo decays at OWPs (lowestorder dynamical decoupling), one must consider clusters of three interacting spins, since independent pairs do not even give finite T2 decay times. We show that while operating near OWPs, dynamical decoupling sequences require hundreds of pulses for a single order of magnitude enhancement of T2, in contrast to regimes far from OWPs, where only about ten pulses are required.