  In this paper we construct a new type of cavity array, in each cavity of
which multiple two-level atoms interact with two independent photon modes. This
system can be totally governed by a two-mode Dicke-lattice model, which
includes all of the counter-rotating terms and therefore works well in the
ultrastrong coupling regime achieved in recent experiments. Attributed to its
special atom-photon coupling scheme, this model supports a global conserved
excitation and a continuous $U(1)$ symmetry, rather than the discrete $Z_{2}$
symmetry in the standard Dicke-lattice model. This distinct change of symmetry
via adding an extra photon mode strongly impacts the nature of photon
localization/delocalization behavior. Specifically, the atom-photon interaction
features stable Mott-lobe structures of photons and a second-order
superfluid-Mott-insulator phase transition, which share similarities with the
Jaynes-Cummings-lattice and Bose-Hubbard models. More interestingly, the
Mott-lobe structures predicted here depend crucially on the atom number of each
site. We also show that our model can be mapped into a continuous $XX$ spin
model. Finally, we propose a scheme to implement the introduced cavity array in
circuit quantum electrodynamics. This work broadens our understanding of
strongly-correlated photons.
