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

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