Photon-assisted Landau-Zener transitions in a periodically driven Rabi dimer coupled to a dissipative mode

We investigate multiple photon-assisted Landau-Zener (LZ) transitions in a hybrid circuit quantum electrodynamics device in which each of two interacting transmission-line resonators is coupled to a qubit, and the qubits are driven by periodic driving fields and also coupled to a common phonon mode. The quantum state of the entire composite system is modeled using the multi-D₂Ansatz in combination with the time-dependent Dirac-Frenkel variational principle. Applying a sinusoidal driving field to one of the qubits, this device is an ideal platform to study the photon-assisted LZ transitions by comparing the dynamics of the two qubits. A series of interfering photon-assisted LZ transitions takes place if the photon frequency is much smaller than the driving amplitude. Once the two energy scales are comparable, independent LZ transitions arise and a transition pathway is revealed using an energy diagram. It is found that both adiabatic and nonadiabatic transitions are involved in the dynamics. Used to model environmental effects on the LZ transitions, the common phonon mode coupled to the qubits allows for more available states to facilitate the LZ transitions. An analytical formula is obtained to estimate the short time phonon population and produces results in reasonable agreement with numerical calculations. Equipped with the knowledge of the photon-assisted LZ transitions in the system, we can precisely manipulate the qubit state and successfully generate the qubit dynamics with a square-wave pattern by applying driving fields to both qubits, opening up new venues to manipulate the states of qubits and photons in quantum information devices and quantum computers.