  Recent progress on qubit manipulation allows application of periodic driving
signals on qubits. In this study, a harmonic driving field is added to a Rabi
dimer to engineer photon and qubit dynamics in a circuit quantum
electrodynamics device. To model environmental effects, qubits in the Rabi
dimer are coupled to a phonon bath with a sub-Ohmic spectral density. A
non-perturbative treatment, the Dirac-Frenkel time-dependent variational
principle together with the multiple Davydov D$_2$ {\it Ansatz} is employed to
explore the dynamical behavior of the tunable Rabi dimer. In the absence of the
phonon bath, the amplitude damping of the photon number oscillation is greatly
suppressed by the driving field, and photons can be created thanks to
resonances between the periodic driving field and the photon frequency. In the
presence of the phonon bath, one still can change the photon numbers in two
resonators, and indirectly alter the photon imbalance in the Rabi dimer by
directly varying the driving signal in one qubit. It is shown that qubit states
can be manipulated directly by the harmonic driving. The environment is found
to strengthen the interqubit asymmetry induced by the external driving, opening
up a new venue to engineer the qubit states.
