  We develop a general theory to study the electromagnetically induced
transparency (EIT) in ultracold quantum gases, applicable for both Bose and
Fermi gases with arbitrary inter-particle interaction strength. We show that,
in the weak probe field limit, the EIT spectrum is solely determined by the
single particle Green's function of the ground state atoms, and reflects
interesting quantum many-body effects when atoms are virtually coupled to the
low-lying Rydberg states. As an example, we apply our theory to 1D Luttinger
liquid, Bose-Mott insulator state, and the superfluid state of two-component
Fermi gases, and show how the many-body features can be observed
non-destructively in the unconventional EIT spectrum.
