Multiphonon-resonance quantum Rabi model and adiabatic passage in a cavity-optomechanical system

In this paper, we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system. In the scheme, when the driving bichromatic laser beam is adjusted to the off-resonant j-order red- and blue-sideband, the interaction between the cavity and mechanical oscillator leads to a j-phonon resonance quantum Rabi model. Moreover, we show that there exists a resonant multi-phonon coupling via intermediate states connected by counter-rotating processes when the frequency of the simulated bosonic mode is near a fraction of the transition frequency of the simulated two-level system. As a typical example, we theoretically analyze the two-phonon resonance quantum Rabi model, and derive an effective Hamiltonian of the six-phonon coupling. Finally, we present a method of six-phonon generation based on adiabatic passage across the resonance. Numerical simulations confirm the validity of the proposed scheme. Theoretically, the proposed scheme can be extended to the realization of 3j-phonon state.