We show how spin-spin correlations, detected in a non-destructive way via spatially resolved quantum polarization spectroscopy, strongly characterize various phases realized in trapped ultracold fermionic atoms. Polarization degrees of freedom of the light couple to spatially resolved components of the atomic spin. In this way, quantum fluctuations of matter are faithfully mapped onto those of light. In particular, we demonstrate that quantum spin polarization spectroscopy provides a direct method to detect the Fulde-Ferrell-Larkin-Ovchinnikov phase realized in a one-dimensional imbalanced Fermi system. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.