  New schemes that exploit the unique properties of Nitrogen-Vacancy (NV)
centers in diamond are presently being explored as a platform for
high-resolution magnetic sensing. Here we focus on the ability of a NV center
to monitor an adjacent mesoscopic nuclear spin bath. For this purpose, we
conduct comparative experiments where the NV spin evolves under the influence
of surrounding 13C nuclei or, alternatively, in the presence of asynchronous AC
fields engineered to emulate bath fluctuations. Our study reveals substantial
differences that underscore the limitations of the semi-classical picture when
interpreting and predicting the outcome of experiments designed to probe small
nuclear spin ensembles. In particular, our study elucidates the NV center
response to bath fluctuations under common pulse sequences, and explores a
detection protocol designed to probe time correlations of the nuclear spin bath
dynamics. Further, we show that the presence of macroscopic nuclear spin order
is key to the emergence of semi-classical spin magnetometry.
