Group theoretical analysis of nitrogen-vacancy center’s energy levels and selection rules

We use a group theoretical approach to model the nitrogen-vacancy defect in diamond. In our analysis we clarify several properties of this defect that have been source of controversy such as the ordering of the singlets and the mechanism that leads to spin mixing in the excited state of this defect. In particular, we demonstrate that the ordering of the ground state configuration (e2) is {3A2, 1E, 1A1} and that the spin-spin interaction causes the mixing in the excited state. In addition, we analyze the angular momentum and spin properties of the excited state structure that enables a spin photon entanglement scheme that has been recently demonstrate experimentally. Our description is general and it can be easily applied to other defects in solid-state systems.