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In this paper, we investigate the energy spectrum and coherent dynamicalprocess in a cavity-QED setup with a moving emitter, which is subject to aharmonic potential. We find that the vibration of the emitter will induce theeffective Kerr and optomechanical interactions. We generalize the Bogliubovoperators approach which dealt with quantum Rabi model, to ourcavity-emitter-vibration system and obtain the energy spectrum exactly. Withthe assistance of Bogliubov operators approach, we obtain the energy spectrumof the system exactly. Furthermore, we show that the dynamics of the systemexhibit a two-frequency Rabi oscillation behavior. We explain such behavior byoptomechanical interaction induced quantum transition between emitter-cavitydressed states. We hope that the interaction between cavity mode and movingemitter will provide a versatile platform to explore more exotic effects andpotential applications in cavity-QED scenario.

Exact solvability and two-frequency Rabi oscillation in cavity-QED setup with moving emitter