Two-photon process of a single two-level atom simultaneously absorbing or emitting two photons distributed in different cavities and its applications

We propose an approach for achieving a two-photon process in which a single two-level atom can simultaneously absorb or emit two photons separately distributed in two cavities. This two-photon process is realized by a two-level atom dispersively coupled to a classical pulse and two cavities. The main advantage of this proposal lies in the fact that because only two levels of the atom are used, i.e., no auxiliary atomic levels are utilized, decoherence from the higher energy levels of the atom is avoided. In addition, we find that the two-photon process can enable the synthesis of a hybrid atom-cavity-cavity Greenberger-Horne-Zeilinger (GHZ) entangled state. As an example, we further discuss the experimental feasibility of creating the proposed hybrid GHZ state in a circuit QED system. This proposal is quite general and can be implemented in a wide range of physical systems, such as a natural or artificial atom coupled to two optical or microwave cavities.