Effect of atomic diffusion on spin noise spectroscopy with a tightly focused beam

Atomic diffusion can limit the sensitivity of atomic sensors and optical magnetometers. Here we introduce an analytical model for explaining the atomic diffusion component of the spin time-correlation function under different conditions of beam focusing and buffer gas pressure. For a tightly focused probe beam we find that the decay of the diffusion correlation function follows a power law rather than exponential, as it does in the collimated case. Counter-intuitively, this results in a narrowing of the spin-noise linewidth and significant increase in the noise peak amplitude. We are currently performing experimental measurements of the atomic diffusion effects in the spin noise spectra as a function of probe beams focus size down to 2 $\mu $m and as a function of the buffer gas pressure. We will present detailed comparison of theory and experiment and discuss implications of the atomic diffusion on sub-shot noise measurements in atomic sensors.