Figure 1. MW-driven ¹³C polarization derived from optically pumped nitrogen-vacancy centres.

(a) Spin-1 NV electronic defect strongly coupled to a ¹³C nucleus (black circle), irradiated simultaneously by MW (orange lightning bolt) and laser fields (green beam). The optically pumped NV-spin (green sphere) transfers its polarization to the coupled nucleus (dark blue sphere) and eventually to the remaining ¹³C (the bulk) by interactions within a dipolar spin network (light blue spheres). The red spheres are unpolarized nuclei. (b) Energy-level diagram of the electron defect, hyperfine coupled to a ¹³C in presence of a potential magnetic field B₀ (without MW fields). The dashed box shows the energy levels addressed, and stresses an initial state containing equal populations on the lower , eigenstates after optical pumping. (c) Spin dynamical regimes determined by the relation between the MW power and the energy splittings. The solid black lines only represent the eigenstates , , and of the system in the selective regime; in the remaining cases these lines represent states , , and that are relevant for the MW selection rules, but where and are linear superpositions of the eigenstates and . Blue vertical arrows represent the MW excitation on resonance with the transition , circular green arrows represent an effective Larmor precession with frequency δ, while curly red arrows represent a laser-induced relaxation-like process conserving the nuclear spin state but driving the incoherent optical pumping52. The filled and coloured circles schematize the populations of each state resulting from these dynamics. Although not explicitly shown in these energy-level diagrams, the electronic and nuclear spins involved in these manifolds are also coupled by dipole–dipole interactions to the ¹³C ensemble via a spin-coupling network, enabling further polarization transfers to the bulk (a).