Abstract
We develop a general theory to study the electromagnetically induced transparency (EIT) in ultracold quantum gases, applicable for both Bose and Fermi gases with an arbitrary interparticle 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 a one-dimensional Luttinger liquid, a Bose-Mott insulator state, and the superfluid state of two-component Fermi gases, and show how the many-body features can be observed nondestructively in the unconventional EIT spectrum. © 2013 American Physical Society.