Sensing diffusion with spin-centers*

In this work we study the electric noise in spin defects due to both fluctuation of the surface charge density and the electrostatic potential at the surface of a crystal. Surprisingly, we show 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 and the surface electrostatic potential, rather than solely by the character of the charge fluctuators, e.g., point-like or dipole. Furthermore, the theory developed here identifies the fingerprints and signatures of diffusion of charged particles in the spin defect's T1 and T2. Similarly to some many-body sensing techniques, here both the defect spin decay and dephasing contain a crossover as a function of time around the characteristic correlation time of the fluctuators, determined by the diffusion coefficients. Hence, spin defects can also be used for sensing  diffusion phenomena and extracting the corresponding correlation time and diffusion constant.