"Galton board" nuclear hyperpolarization

TL;DR

This paper introduces a novel theoretical model for hyperpolarization transfer in electron-nuclear spin systems using a Galton board analogy, enabling better understanding and potential applications in quantum sensing and DNP.

Contribution

It develops a new analytical framework mapping Landau-Zener crossings to a Galton board, providing insights into polarization dynamics in coupled electron-nuclear systems.

Findings

The model accurately describes polarization transfer at spectral line wings.

Application to NV centers in diamond demonstrates practical relevance.

The approach offers an intuitive understanding of complex spin dynamics.

Abstract

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 13C 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.