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

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