Enhancing the polarization of nuclear spins surrounding the nitrogen-vacancy(NV) center in diamond has attracted widespread attention recently due to itsvarious applications. Here we present an analytical theory and comprehensiveunderstanding on how to optimize the dynamic nuclear polarization by anoptically pumped NV center near the ground state level anticrossing. Ourresults not only provide a parameter-free explanation and a clearly physicspicture for the recently observed polarization dependence on the magnetic fieldfor strongly coupled $^{13}$C nuclei [H. J. Wang \textit{et al}., Nat. Commun.4, 1 (2013)], but also demonstrate the possibility to strongly polarize weaklycoupled $^{13}$C nuclei under weak optical pumping and suitably chosen magneticfield. This allows sensitive magnetic control of the $^{13}$C nuclear spinpolarization for NMR applications and significant suppression of the $^{13}$Cnuclear spin noise to prolong the NV spin coherence time.
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