  We study the fundamental limits of noise spectroscopy using estimation
theory, Faraday rotation probing of an atomic spin system, and squeezed light.
We find a simple and general expression for the Fisher information, which
quantifies the sensitivity to spectral parameters such as resonance frequency
and linewidth. For optically-detected spin noise spectroscopy, we find that
shot noise imposes "local" standard quantum limits for any given probe power
and atom number, and also "global" standard quantum limits when probe power and
atom number are taken as free parameters. We confirm these estimation theory
results using non-destructive Faraday rotation probing of hot Rb vapor,
observing the predicted optima and finding good quantitative agreement with a
first-principles calculation of the spin noise spectra. Finally, we show
sensitivity beyond the atom- and photon-number-optimized global standard
quantum limit using squeezed light.
