Interference effects on quantum light group velocity in cavity induced transparency

We investigate the propagation of a quantized probe field in a dense medium composed of three-level Λ-type systems under cavity electromagnetically induced transparency conditions. We treat the medium as composed of collective states of the three-level systems while the light-medium interaction occurs within clusters of such collective states depending on the photon number state of the probe field. We observe slower group velocity for lower photon number input probe field only under conditions of no interference between different clusters of collective states in the system.