Bell state generation of multi-level systems in the presence of complex entangling interactions

In this paper, we extend our previous theoretical work on the partitioning of entangling interactions of two-level bipartite or two-mode physical and chemical systems to three-level systems. The partitioning is based on the rotating wave approximation (RWA) usually employed for the research on the interaction between physical and chemical systems, and electromagnetic fields. We propose a method of creating the Bell states from the initial separable state in the presence of complicated entangling interactions in three-level bipartite systems. The point is to annihilate the laser-matter and entangling interactions between the Hilbert space of interest and that outside of it by using the rapidly rotating terms in RWA. The procedure proposed in this work will be one of the guidelines of the entanglement generation in the presence of complicated entangling interactions in molecular systems.