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Recent progress on qubit manipulation allows application of periodic drivingsignals on qubits. In this study, a harmonic driving field is added to a Rabidimer to engineer photon and qubit dynamics in a circuit quantumelectrodynamics device. To model environmental effects, qubits in the Rabidimer are coupled to a phonon bath with a sub-Ohmic spectral density. Anon-perturbative treatment, the Dirac-Frenkel time-dependent variationalprinciple together with the multiple Davydov D$_2$ {\it Ansatz} is employed toexplore the dynamical behavior of the tunable Rabi dimer. In the absence of thephonon bath, the amplitude damping of the photon number oscillation is greatlysuppressed by the driving field, and photons can be created thanks toresonances between the periodic driving field and the photon frequency. In thepresence of the phonon bath, one still can change the photon numbers in tworesonators, and indirectly alter the photon imbalance in the Rabi dimer bydirectly varying the driving signal in one qubit. It is shown that qubit statescan be manipulated directly by the harmonic driving. The environment is foundto strengthen the interqubit asymmetry induced by the external driving, openingup a new venue to engineer the qubit states.

Dissipative dynamics in a tunable Rabi dimer with periodic harmonic driving