Blueprint for efficient nuclear spin characterization with color centers

Nuclear spins in solids offer a promising avenue for developing scalable quantum hardware. Leveraging nearby single-color centers, these spins can be efficiently addressed at the single-site level through spin resonance. However, characterizing individual nuclear spins is quite cumbersome since the characterization protocols may differ depending on the strength of the hyperfine coupling, necessitating tailored approaches and experimental conditions. While modified electron spin Hahn echoes like Carr-Purcell-Meiboom-Gill (CPMG) and phase cycled CPMG (XY8) pulse sequences are commonly employed, they encounter significant limitations in scenarios involving spin-1/2 systems, strongly coupled spins, or nuclear spin baths comprising distinct isotopes. Here, we present a more straightforward approach for determining the hyperfine interactions among each nuclear spin and the electron spin. This method holds promise across diverse platforms, especially for emerging S=1/2 group IV defects in diamond (e. g. , SiV, GeV, SnV, PbV) and silicon (T center, P donors). We provide a theoretical framework and adapt it for color centers exhibiting various spins. Through simulations conducted on nuclear spin clusters, we evaluate different protocols and compare their performance using the Fisher information matrix and Cram\'er-Rao bounds.