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Experimental noise often contains valuable information on the interactions ofa system with its environment but establishing a relation between the measuredtime fluctuations and relevant physical observables is rarely apparent. Here,we leverage a multi-dimensional and multi-sensor analysis of spectral diffusionto investigate the dynamics of carriers in charge traps surrounding colorcenter clusters in diamond. Working with nitrogen-vacancy (NV) centers sharingthe same diffraction-limited volume, we establish statistical correlations inthe spectral changes we measure as we recursively probe the optical resonancesof the cluster, which we subsequently exploit to unveil proximal traps. Bysimultaneously co-monitoring the spectra of multiple NVs in the set, we showthe ability to deterministically induce Stark shifts in the observed opticalresonances, hence allowing us to identify electrostatically coupled sets ofemitters. These cross-correlated measurements allow us to determine therelative three-dimensional positions of interacting NVs in a cluster as well asthe location and charge sign of proximal traps. Our results can be generalizedto other color centers and open intriguing opportunities for the microscopiccharacterization of photo-carrier dynamics in semiconductors and for themanipulation of nanoscale spin-qubit clusters connected via electric fields.

Correlated spectroscopy of electric noise with color center clusters