  Quantum spin fluctuations provide a unique way to study spin dynamics without
system perturbation. Here we put forward an optical resonance shift spin noise
spectroscopy as a powerful tool to measure the spin noise of various systems
from magnetic impurities in solids to free atoms and molecules. The quantum
spin fluctuations in these systems can shift the optical resonances by more
than the homogeneous linewidth and produce huge Faraday rotation noise. We
demonstrate, that the resonance shift spin noise spectroscopy gives access to
the high order spin correlators, which contain complete information about the
spin dynamics in contrast with the second order correlator measured by
conventional Pauli-blocking spin noise spectroscopy. The high order quantum
spin correlators manifest themselves as a comb of peaks in the Faraday rotation
noise spectra in transverse magnetic field. This effect is closely related with
the multispin flip Raman scattering observed in the Mn-doped nanostructures.
