Quantum Zeno and Zeno-like effects in nitrogen vacancy centers

We present a proposal to realize the quantum Zeno effect (QZE) and quantum Zeno-like effect (QZLE) in a proximal $\mathrm{^{13}C}$ nuclear spin by controlling a proximal electron spin of a nitrogen vacancy (NV) center. The measurement is performed by applying a microwave pulse to induce the transition between different electronic spin states. Under the practical experimental conditions, our calculations show that there exist both QZE and QZLE in a $^{13}$C nuclear spin in the vicinity of an NV center.