  The hyperpolarization of nuclear spins can enable powerful imaging and
sensing techniques provided the hyperpolarization is sufficiently long-lived.
Recent experiments on nanodiamond $^{13}$C nuclear spins demonstrate that
relaxation times can be extended by three orders of magnitude by building up
dynamic nuclear polarization (DNP) through the driving of electron-nuclear
flip-flop processes at defect centers. This finding raises the question of
whether the nuclear spin coherence times are also impacted by this
hyperpolarization process. Here, we theoretically examine the effect of DNP on
the nuclear spin coherence times as a function of the hyperpolarization drive
time. We do this by developing a microscopic theory of DNP in a nuclear spin
ensemble coupled to microwave-driven defect centers in solids and subject to
spin diffusion mediated by internuclear dipolar interactions. We find that,
similarly to relaxation times, the nuclear spin coherence times can be
increased substantially by a few orders of magnitude depending on the driving
time. Our theoretical model and results will be useful for current and future
experiments on enhancing nuclear spin coherence times via DNP.
