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We propose a new method of detecting the onset of superfluidity in atwo-component ultracold fermionic gas of atoms governed by an attractiveshort-range interaction. By studying the two-body correlation functions we findthat a measurement of the momentum distribution of the density and spinresponse functions allows one to access separately the normal and anomalousdensities. The change in sign at low momentum transfer of the density responsefunction signals the transition between a BEC and a BCS regimes, characterizedby small and large pairs, respectively. This change in sign of the densityresponse function represents an unambiguous signature of the BEC to BCScrossover. Also, we predict spin rotational symmetry-breaking in this system

Density and Spin Response Functions in Ultracold Fermionic Atom Gases