Hybrid Rabi interaction with traveling states of light

Hybrid interactions between light and two-level systems and their nonlinear nature are crucial components of advanced quantum information processing and quantum networks. Rabi interaction exhibits the hybrid nonlinear nature, but its implementation is challenging at optical frequencies where the rotating wave approximation (RWA) is valid. Here, we propose a setup to conditionally induce Rabi interaction between discrete variable and continuous variable of traveling beams of light. We show that our scheme can generate Rabi interaction on weak states of light, where signatures of the nonlinear quantum effects are preserved for typical experimental losses. These results prove that a hybrid Rabi interaction can be realized in all-optical setups, and open a way to experimental investigations of nonlinear quantum optics beyond RWA.