Quantum Memory on ¹³C–¹³C Dimers in Diamond with NV Centers: Simulation by Quantum Chemistry Methods

Individual electron–nuclear spin systems in solids are promising platforms for implementation of second-generation quantum technologies. The recognized leader among such systems is the negatively charged nitrogen–vacancy color center (NV center) in diamond with hyperfine coupling to nuclear spins of carbon-13 (¹³C), which are widely used as a quantum memory in emerging quantum technologies because of their weak interaction with the environment. Recently, pairs of ¹³C–¹³C nuclei (dimers) in diamond with NV centers have been proposed and actively studied for this purpose because they have extremely long coherence times (minutes at room temperature) in the singlet state. The eigenstates of the spin Hamiltonian of the NV–¹³C–¹³C system were found and used to calculate the probabilities of EPR transitions between nuclear-spin sublevels of NV-center states with electron spin projections m_S = 0 and m_S = –1. The obtained expressions form the basis for choosing the optimal parameters of microwave and radiofrequency pulses transforming a particular dimer into the singlet state. An example of such a prediction for a specific NV–¹³C–¹³C spin system using data for the spatial positions of the ¹³C spins and the internal spin–spin couplings obtained earlier by quantum chemistry methods is presented.