  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.
