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We consider the problem of determining the spectrum of an electronic spin via polarization transfer to coupled nuclear spins and their subsequent readout. This suggests applications for employing dynamic nuclear polarization (DNP) for "ESR-via-NMR". In this paper, we describe the theoretical basis for this process by developing a model for the evolution dynamics of the coupled electron-nuclear system through a cascade of Landau-Zener anti-crossings (LZ-LACs). We develop a method to map these traversals to the operation of an equivalent "Galton board". Here, LZ-LAC points serve as analogues to Galton board "pegs", upon interacting with which the nuclear populations redistribute. The developed hyperpolarization then tracks the local electronic density of states. We show that this approach yields an intuitive and analytically tractable solution of the polarization transfer dynamics, including when DNP is carried out at the wing of a homogeneously broadened electronic spectral line. We apply this approach to a model system comprised of a Nitrogen Vacancy (NV) center electron in diamond, hyperfine coupled to N neighboring 13 C nuclear spins, and discuss applications for nuclear-spin interrogated NV center magnetometry. More broadly, the methodology of "one-to-many" electron-to-nuclear spectral mapping developed here suggests interesting applications in quantum memories and sensing, as well as wider applications in modeling DNP processes in the multiple nuclear spin limit.

Rapid injection of spin polarization into an ensemble of nuclear spins is a problem of broad interest, spanning dynamic nuclear polarization (DNP) to quantum information science. We report on a strategy to boost the spin injection rate by exploiting electrons that can be rapidly polarized via high-power optical pumping. We demonstrate this in a model system of Nitrogen Vacancy center electrons injecting polarization into a bath of 13 C nuclei in diamond. We innovate an apparatus with thirty lasers to deliver >20W of continuous, nearly isotropic, optical power to the sample with only a minimal temperature increase. This constitutes a substantially higher power than in previous experiments, and through a spin-ratchet polarization transfer mechanism, yields boosts in spin injection rates by over two orders of magnitude. Our experiments also elucidate speed-limits of nuclear spin injection that are individually bottlenecked by rates of electron polarization, polarization transfer to proximal nuclei, and spin diffusion. This work demonstrates opportunities for rapid spin injection employing non-thermally generated electron polarization, and has relevance to a broad class of experimental systems including in DNP, quantum sensing, and spin-based MASERs.

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