  Nitrogen vacancy (NV) centers in diamond are atom-scale defects with long
spin coherence times that can be used to sense magnetic fields with high
sensitivity and spatial resolution. Typically, the magnetic field projection at
a single point is measured by averaging many sequential measurements with a
single NV center, or the magnetic field distribution is reconstructed by taking
a spatial average over an ensemble of many NV centers. In averaging over many
single-NV center experiments, both techniques discard information. Here we
propose and implement a new sensing modality, whereby two or more NV centers
are measured simultaneously, and we extract temporal and spatial correlations
in their signals that would otherwise be inaccessible. We analytically derive
the measurable two-point correlator in the presence of environmental noise,
quantum projection noise, and readout noise. We show that optimizing the
readout noise is critical for measuring correlations, and we experimentally
demonstrate measurements of correlated applied noise using spin-to-charge
readout of two NV centers. We also implement a spectral reconstruction protocol
for disentangling local and nonlocal noise sources, and demonstrate that
independent control of two NV centers can be used to measure the temporal
structure of correlations. Our covariance magnetometry scheme has numerous
applications in studying spatiotemporal structure factors and dynamics, and
opens a new frontier in nanoscale sensing.
