Identity Test of Single NV^{-} Centers in Diamond at Hz-Precision Level

Atomiclike defects in solids are not considered to be identical owing to the imperfections of host lattice. Here, we found that even under ambient conditions, negatively charged nitrogen-vacancy (NV^{-}) centers in diamond could still manifest identical at Hz-precision level, corresponding to a 10^{-7}-level relative precision, while the lattice strain can destroy the identity by tens of Hz. All parameters involved in the NV^{-}-^{14}N Hamiltonian are determined by formulating six nuclear frequencies at 10-mHz-level precision and measuring them at Hz-level precision. The most precisely measured parameter, the ^{14}N quadrupole coupling P, is given by -494 575 4.9(8)  Hz, whose precision is improved by nearly 4 orders of magnitude compared with previous measurements. We offer an approach for performing precision measurements in solids and deepening our understandings of NV centers as well as other solid-state defects. Besides, these high-precision results imply a potential application of a robust and integrated atomiclike clock based on ensemble NV centers.