  Dephasing and relaxation of the nuclear spins coupled to the nitrogen-vacancy
(NV) center during optical initialization and readout is an important issue for
various applications of this hybrid quantum register. Here we present both an
analytical description and a numerical simulation for this process, which agree
reasonably with the experimental measurements. For the NV center under cyclic
optical transition, our analytical formula not only provide a clear physics
picture, but also allows controlling the nuclear spin dissipation by tuning an
external magnetic field. For more general optical pumping, our analytical
formula reveals significant contribution to the nuclear spin dissipation due to
electron random hopping into/out of the $m=0$ (or $m=\pm1$) subspace. This
contribution is not suppressed even under saturated optical pumping and/or
vanishing magnetic field, thus providing a possible solution to the puzzling
observation of nuclear spin dephasing in zero perpendicular magnetic field [M.
V. G. Dutt \textit{et al}., Science \textbf{316}, 1312 (2007)]. It also implies
that enhancing the degree of spin polarization of the nitrogen-vacancy center
can reduce the effect of optical induced nuclear spin dissipation.
