Measuring nuclear spin qubits by qudit-enhanced spectroscopy in Silicon Carbide

Nuclear spins with hyperfine coupling to single electron spins are highly valuable quantum bits. In this work we probe and characterise the particularly rich nuclear spin environment around single silicon vacancy color-centers (V2) in 4H-SiC. By using the electron spin-3/2 qudit as a 4 level sensor, we identify several groups of $^{29}$Si and $^{13}$C nuclear spins through their hyperfine interaction. We extract the major components of their hyperfine coupling via optical detected nuclear resonance, and assign them to shell groups in the crystal via the DFT simulations. We utilise the ground state level anti-crossing of the electron spin for dynamic nuclear polarization and achieve a nuclear spin polarization of up to $98\pm6\,\%$. We show that this scheme can be used to detect the nuclear magnetic resonance signal of individual spins and demonstrate their coherent control. Our work provides a detailed set of parameters for future use of SiC as a multi-qubit memory and quantum computing platform.