Defects in solids with spins (also known as spin centers) have been shown as promising room temperature solid-state qubits with the ability to be optically initialized and interrogated[1]. Additionally, they have also been demonstrate to be great non-evasive quantum sensors due to their high energy levels sensitivity to both magnetic and electric fields. In general, static electromagnetic fields can be inferred from the shift of the emitted spin center photoluminescence, while dynamical fluctuating fields (generating noise) are inferred from the change of the spin center coherence times[2].

Here we study the electric noise in spin defects due to both fluctuation of the surface charged density and the electrostatic potential at the surface of our crystal [3]. Surprisingly, we show in Fig. 1 that the depth dependence of the electric noise spectral density is strongly influenced by the two-point correlation function of both the charged particles’ positions, rather than solely by the character of the charge fluctuators, e.g., point-like or dipole. Furthermore, we are able to recognize the fingerprints and signatures of diffusion phenomena of charged particles through the spin defect’s T1 and T2. This is seen on both the defect spin decay and dephasing containing a crossover as function of time around the characteristic correlation time of the fluctuators, determined by the diffusion coefficients (Fig. 2). Hence, spin defects can also be used for sensing of diffusion phenomena and extraction of its corresponding correlation time and diffusion constant.

Work supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award DE-SC0021314.

[1] D. D. Awschalom, R. Hanson, J. Wrachtrup,and B. B. Zhou, Nature Photonics12, 516 (2018).
[2] R. Schirhagl, K. Chang, M. Loretz, and C. L. Degen, Annual Review of Physical Chemistry 65, 83 (2014).
[3] D. R. Candido and M. E. Flatté, arXiv:2112.15581 (2021).

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 shallow 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.