Correlation function of spin noise due to atomic diffusion

TL;DR

This paper derives analytical models for the spin noise spectrum in atomic vapors with diffusion, validated by experiments showing pressure-independent lineshapes in focused beams.

Contribution

It introduces new analytical expressions for the diffusion-related spin noise spectrum in focused Gaussian beams, supported by experimental validation.

Findings

Analytical forms for spin noise correlation functions and spectra in focused beams.

Good agreement between theory and experiment across various N2 pressures.

Spectral lineshape independence from buffer gas pressure in tightly focused beams.

Abstract

We use paramagnetic Faraday rotation to study spin noise spectrum from unpolarized Rb vapor in a tightly focused probe beam in the presence of N$_2$ buffer gas. We derive an analytical form for the diffusion component of the spin noise time-correlation function in a Gaussian probe beam. We also obtain analytical forms for the frequency spectrum of the spin noise in the limit of a tightly focused or a collimated Gaussian beam in the presence of diffusion. In particular, we find that in a tightly focused probe beam the spectral lineshape can be independent of the buffer gas pressure. Experimentally, we find good agreement between the calculated and measured spin noise spectra for N$_2$ gas pressures ranging from 56 to 820 torr.