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 29Si impurities which provides the dominant decoherence mech
anism (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 suggest that anisotropic contributions are comparatively weak, so the form of the divergences is largely independent of crystal orientation.
There is growing interest in bismuth-doped silicon (Si:Bi) as an alternative to the well-studied proposals for silicon based quantum information processing (QIP) using phosphorus-doped silicon (Si:P). We focus here on the implications of its anomalou
sly strong hyperfine coupling. In particular, we analyse in detail the regime where recent pulsed magnetic resonance experiments have demonstrated the potential for orders of magnitude speedup in quantum gates by exploiting transitions that are electron paramagnetic resonance (EPR) forbidden at high fields. We also present calculations using a phenomenological Markovian master equation which models the decoherence of the electron spin due to Gaussian temporal magnetic field perturbations. The model quantifies the advantages of certain optimal working points identified as the $df/dB=0$ regions, where $f$ is the transition frequency, which come in the form of frequency minima and maxima. We show that at such regions, dephasing due to the interaction of the electron spin with a fluctuating magnetic field in the $z$ direction (usually adiabatic) is completely removed.
