Characterization of the internal state of NV center in diamond and second quantization formalism

In this paper a general study of NV center internal state in diamond is presented. This study is based on experimental and theoretical findingsfound in literature. First, a Hamiltonian model for center NV internal state is proposed in terms of a complete set of commuting observables(CSCO), which consist of angular momentum ^L, spin momentum ^ S, total angular momentum ^ J = ^L+ ^ S and spin momentum on z-direction^ Sz. The second quantization formalism –in steady-state (conservative model)– is used. The creation and annihilation operators are used todescribed the steady spin-levels structure and in dynamic-state (non-conservative model) and can also describe the system dynamic betweendifferent spin-levels transitions. Finally, a discussion is presented about the application of this study in the photochromism phenomenon andsolid-state quantum bit (qubit).