Photon emission via vacuum-dressed intermediate states under ultrastrong coupling

We investigate theoretically quantum effects of a cavity-atom system in which the upper two levels of a cascade-type three-level atom interact with a cavity field mode in the ultrastrong-coupling regime. By exploiting the virtual photons carried by atom-cavity dressed states, we indicate how two external driving fields induce Raman transitions such that a cavity photon pair can be generated with a high probability. We present analytical and numerical solutions of the system and determine the rate of photons transmitted out of the cavity. In addition, we show that the transmitted photons exhibit a bunching behavior in the steady state. Our scheme demonstrates that atom-cavity dressed states in the ultrastrong-coupling regime can serve as intermediate states to invoke nonlinear optical processes.