  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 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.
