In this paper, by using J-C model and the density operator theory in interaction picture, we studied the evolution features of linear entropy in the system of two two-level Rydberg atom and two entangled dissipative cavities with single-photon resonant interaction. With derivation and numerical calculation of the linear entropies of a single atom, a single cavity, as well as two atoms, two cavities, we got some results of quantum entangling degree's evolution on the atoms and cavities in this system, and we analyzed how the cavity dissipation coefficients and the atom-cavity interaction coupling coefficient influenced the oscillation model and the evolution period of linear entropies.
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