Bath-limited dynamics of nuclear spins in solid-state spin platforms

Nuclear spins in the proximity of electronic spin defects in solids are promising platforms for quantum information processing due to their ability to preserve quantum states for a remarkably long time. Here we report a comprehensive ab initio study of the nuclear spin dynamics in solid-state systems. First, we characterize spin exchange-dependent oscillations of the Hahn-echo signal of the single nuclear spins in isonuclear spin baths pointing at a new sensing modality of dynamical-decoupling spectroscopy. Using first-principles simulations, we then quantify the enhancement in the coherence of nuclear spins as a function of distance and state of the electron spin and validate our results with experimental data for the nitrogen vacancy in diamond. Finally, we describe how hybridization of the electronic states suppresses the coherence time of strongly coupled nuclear spins and how dynamical changes of the electron spin state may deteriorate nuclear coherence. The computational framework developed in our work is general and can be broadly applied to predict the dynamical properties of nuclear spins in a wide variety of systems. Overall, our results elucidate many pitfalls that should be avoided to preserve the nuclear spin state in solid-state systems.