Creation and dynamics of spin fluctuations in a noisy magnetic field

Abstract

We theoretically and numerically investigate the spin fluctuations induced in a
thermal atomic ensemble by an external fluctuating uniaxial magnetic field, in the
context of a standard spin noise spectroscopy (SNS) experiment. We show that
additional spin noise is excited, which dramatically depends on the magnetic noise
variance and bandwidth, as well as on the power of the probe light and its polarization
direction. We develop an analytical perturbative model proving that this spin noise first
emerges from the residual optical pumping in the medium, which is then converted into
spin fluctuations by the magnetic noise and eventually detected using SNS. The system
studied is a spin-1 system, which thus shows both Faraday rotation and ellipticity noises
induced by the random magnetic fluctuations. The analytical model gives results
in perfect agreement with the numerical simulations, with potential applications in
future experimental characterization of stray field properties and their influence on
spin dynamics.