Slow-light probe of Fermi pairing through an atom-molecule dark state

We consider the two-color photoassociation of a quantum degenerate atomic gas into ground-state diatomic molecules via a molecular dark state. This process can be described in terms of a Λ level scheme that is formally analogous to the situation in electromagnetically induced transparency in atomic systems and therefore can result in slow-light propagation. We show that the group velocity of the light field depends explicitly on whether the atoms are bosons or fermions, as well as on the existence or absence of a pairing gap in the case of fermions, so that the measurement of the group velocity realizes a nondestructive diagnosis of the atomic state and the pairing gap.