Coherent control of nitrogen nuclear spins via the V$_B^-$-center in hexagonal boron nitride

Abstract: Charged boron vacancies (V$\text{B}^-$) in hexagonal boron nitride (hBN) have emerged as a promising platform for quantum nanoscale sensing and imaging. While these primarily involve electron spins, nuclear spins provide an additional resource for quantum operations. This work presents a comprehensive experimental and theoretical study of the properties and coherent control of the nearest-neighbor $^{15}$N nuclear spins of V$\text{B}^-$-ensembles in isotope-enriched h$^{10}$B$^{15}$N. Multi-nuclear spin states are selectively addressed, enabled by state-specific nuclear spin transitions arising from spin-state mixing. We perform Rabi driving between selected state pairs, define elementary quantum gates, and measure longer than 10~$\mu$s nuclear Rabi coherence times. We observe a two orders of magnitude nuclear g-factor enhancement that underpins fast nuclear spin gates. Accompanying numerical simulations provide a deep insight into the underlying mechanisms. These results establish the foundations for leveraging nuclear spins in V$_\text{B}^-$ center-based quantum applications, particularly for extending coherence times and enhancing the sensitivity of 2D quantum sensing foils.