Higher order spin noise spectroscopy of atomic spins in fluctuating external fields

TL;DR

This paper investigates how external noisy magnetic fields influence mesoscopic spin fluctuations in atomic systems, revealing that higher order spin cumulants can be significant and measurable using optical spin noise spectroscopy.

Contribution

It introduces a novel analysis of 4th order spin cumulants under external noise and proposes an experiment to measure these cumulants in atomic systems near equilibrium.

Findings

4th order spin cumulant grows as N^2, not suppressed by large N

External noisy fields induce significant higher order spin correlations

Quantitative theory explains experimental observations

Abstract

We discuss the effect of external noisy magnetic fields on mesoscopic spin fluctuations that can be probed in semiconductors and atomic vapors by means of optical spin noise spectroscopy (SNS). We show that conventional arguments of the law of large numbers do not apply to spin correlations induced by external fields, namely, the magnitude of the 4th order spin cumulant grows as $\sim N^2$ with the number $N$ of observed spins, i.e. it is not suppressed in comparison to the 2nd order cumulant. This allows us to design a simple experiment to measure the 4th order cumulant of spin fluctuations in an atomic system near thermodynamic equilibrium and develop quantitative theory that explains all observations.