  In this paper, we consider the transmission characteristics of an optical
cavity loaded with ultra cold atoms in a one dimensional optical lattice at
absolute zero temperature. In particular, we consider the situation when the
many body quantum state of the ultra cold atoms is an insulating state with
fixed number of atoms at each site, which can be either density wave (DW) or
Mott insulator (MI) phase, each showing different type of discrete lattice
translational symmetry. We provide a general framework of understanding the
transmission spectrum from a single and two cavities/modes loaded with such
insulating phases. Further, we also discuss how such a transmission spectrum
changes when these insulating phases make a cross over to the superfluid (SF)
phase with the changing depth of the optical lattice potential.
