Protecting and Dynamically Generating Entanglement in a Two-Atom Two-Field-Mode Model

We analyze the time evolution of quantum entanglement in a model consisting of two two-level atoms interacting with a two-mode electromagnetic field for a variety of initial states. We study two different coupling schemes motivated by the forms that can arise due to atomic separation. We observe a variety of qualitative features such as entanglement sudden death, dynamical generation, protection, and transfer between subsystems. Our quantitative analysis shows that these cases with different couplings and initial states differ significantly in these qualitative features. The multifarious behaviors in these two-mode cases suggest the importance of considering atomic separation carefully for any model where two atoms interact with a common field.