Probing the dynamics of a nuclear spin bath in diamond through time-resolved central spin magnetometry.

Using fast electron spin resonance spectroscopy of a single nitrogen-vacancy defect in diamond, we demonstrate real-time readout of the Overhauser field produced by its nuclear spin environment under ambient conditions. These measurements enable narrowing the Overhauser field distribution by post-selection, corresponding to a conditional preparation of the nuclear spin bath. Correlations of the Overhauser field fluctuations are quantitatively inferred by analysing the Allan deviation over consecutive measurements. This method allows to extract the dynamics of weakly coupled nuclear spins of the reservoir.