The Decoherence of the Electron Spin and Meta-Stability of ¹³C Nuclear Spins in Diamond

Following the recent successful experimental manipulation of entangled ¹³C atoms on the surface of Diamond, we calculate the decoherence of the electron spin in Nitrogen Vacancy NV centers of Diamond via a nonperturbative treatment of the time-dependent Greens function of a Central-Spin model in order to identify the Replica Symmetry Breaking mechanism associated with intersystem mixing between the m_s = 0 sublevel of the ³A₂ and ¹A₁ states of the NV⁻ centers, which we identify as mediated via the meta-stability of 13C nuclei bath processes in our calculations. Rather than the standard exciton-based calculation scheme used for quantum dots, we argue that a new scheme is needed to formally treat the Replica Symmetry Breaking of the ³A₂ → ³E excitations of the NV⁻ centers, which we define by extending the existing Generalized Master Equation formalism via the use of fractional time derivatives. Our calculations allow us to accurately quantify the dangerously irrelevant scaling associated with the Replica Symmetry Breaking and provide an explanation for the experimentally observed room temperature stability of Diamond for Quantum Computing applications.