  Nonequilibrium steady states are investigated in a coupled cavity QED array
system which is pumped by a thermal bath and dissipated through cavity loss. In
the coherent (non-zero photon amplitude) phase, plateau regions appear, where
the steady states become unchanged against the variation of the chemical
potential of the thermal bath. The cavity loss plays a crucial role for the
plateaus: the plateaus appear only if the cavity loss exists, and the photon
leakage current, which is induced by the loss, is essential to the mechanism of
the plateaus.
