Anomalous noise spectra in a spin-exchange-relaxation-free alkali-metal vapor

We perform spin-noise spectroscopy on an unpolarized $^{87}\mathrm{Rb}$ vapor in the spin-exchange-relaxation-free (SERF) regime. We observe noise spectral distributions that deviate strongly from Lorentzian models that accurately describe lower-density regimes. For example, at magnetic fields of $\sim 1 \mathrm{\mu T}$ and $^{87}\mathrm{Rb}$ densities $\gtrsim 1 \times 10^{14} \rm{atoms/cm^{3}}$ we observe an asymmetric spin-noise distribution in which the resonance line is depleted by about half its power, with the diverted power becoming a broad spectral component that could be mistaken for optical shot noise. The results are in good agreement with recent models accounting for correlations between the ground hyperfine states. We discuss implications for quantum sensing and absolute noise calibration in spin-squeezing and entanglement detection.