Correlated spectroscopy of electric noise with color center clusters

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