Nonlinear density scaling of spin noise reveals atomic correlations in warm vapors

We experimentally demonstrate a nonlinear dependence of the spin-noise variance on atomic density in a warm alkali vapor. Implementing high-bandwidth spin-noise spectroscopy (SNS) near the D 2 transition of rubidium, a quadratic spin-noise contribution is shown to arise at high densities, in contrast with the linear dependence valid in noninteracting ensembles. This nonlinear scaling is shown to crucially depend on the residual optical excitation of the vapor by the probe beam, suggesting it stems from atomic cross correlations due to resonant dipole-dipole interaction (ddi) in the vapor. We support this claim by introducing an additional experimental protocol to quench the ddi, resulting in a suppression of both the quadratic scaling of the spin variance and the distortions of the spin-noise spectrum induced by the interaction. These results extend the applications of SNS to the characterization of many-body correlations in complex quantum systems.