Long-range interactions revealed by collective spin noise spectra in atomic vapors

We report anomalous features in the spin noise spectroscopy (SNS) of a thin cell of a dense vapor of alkali atoms. At high densities and close to resonance, we observe a dramatic broadening of the spin noise spectra as well as an unexpected extra low-frequency noise component. With the help of a two-body model and simulations, we show that these features are the hallmark of a strong, long-range dipole-dipole interaction within the ensemble. The additional low-frequency noise reveals the correlated evolution of pair of atoms beyond the impact approximation. In this regime, we demonstrate that spin noise can no longer be obtained from one-body dynamics, opening the way for the characterization of many-body spin noise, atomic entanglement or higher order spin correlators in atomic vapors using SNS.