Active hyperpolarization of the nuclear spin lattice: Application to hexagonal boron nitride color centers

The hyperpolarization of nuclear spin ensembles through their interaction with optically active color centers has emerged as a promising technique with applications ranging from sensing and imaging to quantum computation. Here, we investigate the efficiency of this approach for the hyperpolarization of the nuclear-spin bath in a monolayer of hexagonal boron nitride via the optically active boron vacancy centers (${\mathrm{V}}_{\mathrm{B}}$). To that end we design a polarization sequence based on the suitable combination of optical polarization and microwave driving of the ${\mathrm{V}}_{\mathrm{B}}$, which we optimize numerically. To extend our study to realistic systems with a large number of interacting spins, we employ an approximate method based on the Holstein-Primakoff transformation, whose validity we benchmark against exact numerics for small system sizes. Our results suggest that a high-degree of polarization in the boron and nitrogen nuclear-spin lattices is achievable also at room temperature. Our work provides the first step toward the realization of a two-dimensional quantum simulator based on natural nuclear spins and it can prove useful for extending the coherence time of the ${\mathrm{V}}_{\mathrm{B}}$ centers.