A quantitative study of spin noise spectroscopy in a classical gas of $^{41}$K atoms

TL;DR

This paper derives the electron spin noise power spectrum in alkali gases, applicable to both classical and ultracold quantum gases, and validates the theory with experiments on $^{41}$K atoms showing good agreement.

Contribution

It provides a unified theoretical framework for spin noise spectra in alkali gases and experimentally verifies it for a classical $^{41}$K gas across various magnetic fields.

Findings

Theoretical predictions match experimental measurements for $^{41}$K.

Spin noise spectra are accurately described by electron spin-spin correlation functions.

Agreement persists across a wide range of magnetic field strengths.

Abstract

We present a general derivation of the electron spin noise power spectrum in alkali gases as measured by optical Faraday rotation, which applies to both classical gases at high temperatures as well as ultracold quantum gases. We show that the spin-noise power spectrum is determined by an electron spin-spin correlation function, and we find that measurements of the spin-noise power spectra for a classical gas of $^{41}$K atoms are in good agreement with the predicted values. Experimental and theoretical spin noise spectra are directly and quantitatively compared in both longitudinal and transverse magnetic fields up to the high magnetic field regime (where Zeeman energies exceed the intrinsic hyperfine energy splitting of the $^{41}$K ground state).