  A Rabi dimer is used to model a recently reported circuit quantum
electrodynamics system composed of two coupled transmission-line resonators
with each coupled to one qubit. In this study, a phonon bath is adopted to
mimic the multimode micromechanical resonators and is coupled to the qubits in
the Rabi dimer. The dynamical behavior of the composite system is studied by
the Dirac-Frenkel time-dependent variational principle combined with the
multiple Davydov D$_{2}$ ans\"{a}tze. Initially all the photons are pumped into
the left resonator, and the two qubits are in the down state coupled with the
phonon vacuum. In the strong qubit-photon coupling regime, the photon dynamics
can be engineered by tuning the qubit-bath coupling strength $\alpha$ and
photon delocalization is achieved by increasing $\alpha$. In the absence of
dissipation, photons are localized in the initial resonator. Nevertheless, with
moderate qubit-bath coupling, photons are delocalized with quasiequilibration
of the photon population in two resonators at long times. In this case, high
frequency bath modes are activated by interacting with depolarized qubits. For
strong dissipation, photon delocalization is achieved via frequent
photon-hopping within two resonators and the qubits are suppressed in their
initial down state.
