  We investigate the coherence properties of individual nuclear spin quantum
bits in diamond [Dutt et al., Science, 316, 1312 (2007)] when a proximal
electronic spin associated with a nitrogen-vacancy (NV) center is being
interrogated by optical radiation. The resulting nuclear spin dynamics are
governed by time-dependent hyperfine interaction associated with rapid
electronic transitions, which can be described by a spin-fluctuator model. We
show that due to a process analogous to motional averaging in nuclear magnetic
resonance, the nuclear spin coherence can be preserved after a large number of
optical excitation cycles. Our theoretical analysis is in good agreement with
experimental results. It indicates a novel approach that could potentially
isolate the nuclear spin system completely from the electronic environment.
