Properties of nitrogen-vacancy centers in diamond: the group theoretic approach

We present a procedure that makes use of group theory to analyze and predict the main properties of the negatively charged nitrogen-vacancy (NV) center in diamond. We focus on the relatively low temperature limit where both the spin-spin and spin-orbit effects are important to consider. We demonstrate that group theory may be used to clarify several aspects of the NV structure, such as ordering of the singlets in the (e(2)) electronic configuration and the spin-spin and spin-orbit interactions in the (ae) electronic configuration. We also discuss how the optical selection rules and the response of the center to electric field can be used for spin-photon entanglement schemes. Our general formalism is applicable to a broad class of local defects in solids. The present results have important implications for applications in quantum information science and nanomagnetometry.