Theory of the ground-state spin of the NV- center in diamond

The ground-state spin of the negatively charged nitrogen-vacancy center in diamond has been the platform for the recent rapid expansion of new frontiers in quantum metrology and solid-state quantum-information processing. However, in spite of its many outstanding demonstrations, the theory of the spin has not yet been fully developed, and there do not currently exist thorough explanations for many of its properties, such as the anisotropy of the electron g factor and the existence of Stark effects and strain splittings. In this work, the theory of the ground-state spin is fully developed using the molecular orbital theory of the center in order to provide detailed explanations for the spin's fine and hyperfine structures and its interactions with electric, magnetic, and strain fields. Given these explanations, a general solution is obtained for the spin in any given electric-magnetic-strain field configuration, and the effects of the fields on the spin's coherent evolution, relaxation, and inhomogeneous dephasing are examined. Thus, this work provides the essential theoretical tools for the precise control and modeling of this remarkable spin in its current and future applications.