Quantum Zeno effect in a nitrogen-vacancy center embedded in a spin bath

We study the longitudinal relaxation of a nitrogen-vacancy (NV) center surrounded by a $^{13}$C nuclear spin bath in diamond. By means of cluster-correlation expansion (CCE), we numerically demonstrate the decay process of electronic state induced by cross relaxation at low temperature. It is shown that the CCE method is not only capable of describing pure-dephasing effect at large-detuning regime, but it can also simulate the quantum dynamics of populations in the nearly resonant regime. We present a proposal to slow down the decay of NV center via implementing quantum Zeno effect (QZE). The numerical result shows that QZE can effectively inhibit the decay of NV center.