Spectroscopic Insensitivity to Cold Collisions in a Two-State Mixture of Fermions

We have experimentally demonstrated the absence of spectroscopic resonance shifts in a mixture of two interacting Fermi gases. This result is linked to observations in an ultracold gas of thermal bosons. There, the measured resonance shift due to interstate collisions is independent of the coherence in the system, and twice that expected from the equilibrium energy splitting between the two internal states in a fully decohered cloud. We give a simple theoretical explanation of these observations, which elucidates the effect of coherent radiation on an incoherent mixture of atoms.