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

We study the dynamics of the N-photon entanglement, E(N)(t), for the two-mode Jaynes-Cummings model in the case of a small number N of photons coupled to a single quantum dot inside a cavity, such as a microdisk cavity or a photonic crystal cavity. The quantum dot transitions associated with the photons with different polarizations are assumed to be independent of each other and, hence, the time evolutions of the ' + '- and ' - '-polarized photons are formally separable. However, due to the indistinguishability of the photons, such an interaction still leads to the entanglement of initially disentangled photon states, owing to the nonlinear dependence of the characteristic frequencies on the photon population numbers. The time dependence of the entanglement is the result of superimposing oscillations with incommensurate frequencies. Therefore, E(N)(t) is a quasi-periodic function of time with a complex profile strongly dependent on the number of photons.