  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.
