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We show how spin-spin correlations, detected in a non-destructive way viaspatially resolved quantum polarization spectroscopy, strongly characterizevarious phases realized in trapped ultracold fermionic atoms. Polarizationdegrees of freedom of the light couple to spatially resolved components of theatomic spin. In this way quantum fluctuations of matter are faithfully mappedonto those of light. In particular we demonstrate that quantum spinpolarization spectroscopy provides a direct method to detect theFulde-Ferrell-Larkin-Ovchinnikov phase realized in a one-dimensional imbalancedFermi system.

Quantum polarization spectroscopy of correlations in attractive fermionic gases