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

Identifying insulating states of ultra cold atoms with cavity transmission spectrum