  We analyze the quantum phase transition-like behavior in the lowest energy
state of a two-site coupled atom-cavity system, where each cavity contains one
atom but the total excitation number is not limited to two. Utilizing the
variance of the total excitation number to distinguish the insulator and
superfluid states, and the variance of the atomic excitation number to identify
the polaritonic characteristics of these states, we find that the total
excitation number plays a significant role in the lowest-energy-state phase
transitions. In both the small hopping regime and the small atom-field
interaction regime, we identify an interesting coexisting phase involving
characteristics of both photonic superfluid and atomic insulator. For small
hopping, we find that the signature of the photonic superfluid state becomes
more pronounced with the increase in total excitation number, and that the
boundaries of the various phases shift with respect to the case of $N=2$. In
the limit of small atom-field interaction, the polaritonic superfluid region
becomes broader as the total excitation number increases. We demonstrate that
the variance of the total excitation number in a single site has a linear
dependence on the total excitation number in the large-detuning limit.
