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Complex dynamics of photon entanglement in two-mode Jaynes-Cummings model

We study the dynamics of the photon entanglement, $E_{\mathrm{N}}(t)$, for the two-mode Jaynes-Cummings model in the few-photon case. The atomic transitions associated with the photons with different polarizations are assumed to be independent and, hence, the evolution of the "+"- and "-"-polarized photons is formally separable. However, due to the photons indistinguishability such interaction still leads to entanglement of initially disentangled states owing to the non-linear dependence of the characteristic frequencies on the photon population numbers. The time dependence of entanglement is the result of superimposing oscillations with incommensurate frequencies. Therefore, $E_{\mathrm{N}}(t)$ is a quasi-periodic function of time with the complex profile strongly depending on the number of photons.