Hyperfine Interactions in the NV-¹³C Quantum Registers in Diamond Grown from the Azaadamantane Seed

Nanostructured diamonds hosting optically active paramagnetic color centers (NV, SiV, GeV, etc.) and hyperfine-coupled with them quantum memory ¹³C nuclear spins situated in diamond lattice are currently of great interest to implement emerging quantum technologies (quantum information processing, quantum sensing and metrology). Current methods of creation such as electronic-nuclear spin systems are inherently probabilistic with respect to mutual location of color center electronic spin and ¹³C nuclear spins. A new bottom-up approach to fabricate such systems is to synthesize first chemically appropriate diamond-like organic molecules containing desired isotopic constituents in definite positions and then use them as a seed for diamond growth to produce macroscopic diamonds, subsequently creating vacancy-related color centers in them. In particular, diamonds incorporating coupled NV-¹³C spin systems (quantum registers) with specific mutual arrangements of NV and ¹³C can be obtained from anisotopic azaadamantane molecule. Here we predict the characteristics of hyperfine interactions (hfi) for the NV-¹³C systems in diamonds grown from various isotopically substituted azaadamantane molecules differing in ¹³C position in the seed, as well as the orientation of the NV center in the post-obtained diamond. We used the spatial and hfi data simulated earlier for the H-terminated cluster C₅₁₀[NV]^-H₂₅₂. The data obtained can be used to identify (and correlate with the seed used) the specific NV-¹³C spin system by measuring, e.g., the hfi-induced splitting of the m_S = ±1 sublevels of the NV center in optically detected magnetic resonance (ODMR) spectra being characteristic for various NV-¹³C systems.