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Entanglement in a Jaynes-Cummings Model with Two Atoms and Two Photon Modes

We investigate the conditions of entanglement for a system of two atoms and two photon modes in vacuum, using the Jaynes-Cummings model in the rotating-wave approximation. It is found, by generalizing the existing results, that the strength of entanglement is a periodic function of time. We explicitly show that our results are in agreement with the existing results of entanglement conditions under appropriate limits. Results for the two-atom and two-photon system are generalized to the case of arbitrary values for the atomic energies, corresponding to photon modes frequencies. Though it is apparently a generalization of the existing work, we have considered for the first time both the resonant and nonresonant conditions and found a general equation which could be true for both cases. Moreover, we show that periodicity of the entanglement is a distinct feature of resonant system. Considering the two atoms and two photons system, in detail, we setup an approach which could be generalized for many particle systems and the resulting master equation can also be analyzed.