Local probing of nuclear bath polarization with a single electronic spin

We demonstrate experimentally that a polarized nuclear spin modifies the dynamic behavior of a neighboring electronic spin. Specifically, an out-of-phase component appears in the electronic spin-echo signal. This component is proportional to the nuclear spin degree of polarization and strongly depends on the nuclear polarization direction. When the electronic spin is surrounded by a polarized nuclear spin bath, the spin-echo quadrature manifests a characteristic frequency related only to the nuclear spins abundance and their collective polarization. We use this analysis to propose a novel measurement method for the local nuclear spin bath of a single electronic spin. We quantify the realistic experimental regimes at which the scheme is efficient. Our proposal has potential applications for quantum sensing schemes, and opens a route for a systematic study of polarized mesoscopical-systems.