  We report on a strategy to indirectly readout the spectrum of an electronic
spin via polarization transfer to nuclear spins in its local environment. The
nuclear spins are far more abundant and have longer lifetimes, allowing
repeated polarization accumulation in them. Subsequent nuclear interrogation
can reveal information about the electronic spectral density of states. We
experimentally demonstrate the method for reading out the ESR spectrum of
Nitrogen Vacancy center electrons in diamond via readout of lattice 13C nuclei.
Spin-lock control on the 13C nuclei yields significantly enhanced
signal-to-noise for the nuclear readout. Spectrally mapped readout presents
operational advantages in being background-free and immune to crystal
orientation and optical scattering. We harness these advantages to demonstrate
applications in underwater magnetometry. The physical basis for the
"one-to-many" spectral map is itself intriguing. To uncover its origin, we
develop a theoretical model that maps the system dynamics, involving traversal
of a cascaded structure of Landau-Zener anti-crossings, to the operation of a
tilted "Galton board". This work points to new opportunities for "ESR-via-NMR"
in dilute electronic systems, and in hybrid electron-nuclear quantum memories
and sensors.
