  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 study of the nuclear decoherence processes in the vicinity of the
nitrogen-vacancy (NV) center in diamond. We simulate from first principles the
change in the dynamics of nuclear spins as a function of distance and state of
the NV center and validate our results with experimental data. Our simulations
reveal nontrivial oscillations in the Hahn echo signal, pointing to a new
sensing modality of dynamical-decoupling spectroscopy, and show how
hybridization of the electronic states suppresses the coherence time of
strongly coupled nuclear spins. The computational framework developed in our
work is general and can be broadly applied to predict the dynamical properties
of nuclear spins.
