  We extend the idea of quantum phase transitions of light in atom-photon
system with Dicke-Bose-Hubbard model for arbitrary number of two-level atoms.
The formulations of eigenenergies, effective Rabi frequencies, and critical
chemical potentials for two atoms are derived. With a self-consistent method,
we obtain a complete phase diagram for two two-level atoms on resonance, which
indicates the transition from Mott insulator to superfluidity and with a mean
excitations diagram for confirmation. We illustrate the generality of the
method by constructing the dressed-state basis for arbitrary number of
two-level atoms. In addition, we show that the Mott insulator lobes in the
phase diagrams will smash out with the increase of atom numbers. The results of
this work provide a step for studying the effects with combinations of
Dicke-like and Hubbard-like models to simulate strongly correlated electron
systems using photons.
