Sensing multiple NV centers for nanoscale covariance magnetometry

Nitrogen vacancy (NV) defect centers in diamond have been used as a versatile platform for nanoscale sensing of many condensed matter systems, but experiments have typically only taken advantage of a single NV center at a time or else performed widefield imaging without nanoscale resolution. Here we discuss what can be learned by simultaneous addressing of multiple NV centers; measuring correlated dynamics in NV centers would provide simultaneous information at two different NV center locations (~0.1 to 100 micron length scales), and optionally at two different sensing times limited only by the experimental clock (~1 ns resolution). Understanding dynamics at these length and time scales is important for many microscopic systems, and measurements of spatiotemporal correlations may provide useful information about the electron mean free path, signatures of hydrodynamic flow, or the nature of local NV center noise sources like surface spins. Assuming two individual NV centers experience a shared 'global' magnetic field as well as noisy 'local' fields, we analytically derive the expected measurable correlation between the sensed signals from the NV centers. We then consider the experimental approach, deriving the sensitivity of such a measurement with a focus on the roles of readout noise and fidelity.