Creation and dynamics of spin fluctuations in a noisy magnetic field

TL;DR

This paper investigates how external magnetic noise influences spin fluctuations in atomic ensembles, revealing the dependence on noise characteristics and probe parameters, with an analytical model matching numerical results.

Contribution

It introduces a perturbative analytical model for spin noise induced by magnetic fluctuations, validated by numerical simulations, applicable to spin noise spectroscopy experiments.

Findings

Spin noise depends on magnetic noise variance and bandwidth.

Optical pumping residuals convert magnetic noise into detectable spin fluctuations.

Analytical results agree with numerical simulations.

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.