Generating three-photon Rabi oscillations without a large-detuning condition

It is well known that in the quantum Rabi model, a three-photon resonance occurs when the cavity field bare frequency is about 1/3 of the atomic transition frequency. In this manuscript, we show that the resonance can also be generated in the absence of the 1/3 condition by employing an artificial atom with tunable transition frequency. To realize the protocol, the modulation frequency should be comparable to the cavity frequency in order to induce a counter-rotating interaction in the effective Hamiltonian. In this way, three-photon Rabi oscillations can be observed in a small-detuning regime, thus avoiding the excitation of high-energy states. We derive an effective Hamiltonian (equivalent to the anisotropic Rabi model Hamiltonian) to determine the magnitude of the energy splitting and the resonance position. Numerical simulations results show that the protocol not only generates a three-photon resonance, but also has a detectable output photon flux. We hope the protocol can be exploited for the realization of Fock-state sources and the generation of multiparticle entanglement.