Dynamics of photon-photon entanglement in a bimodal nonlinear nanocavity

The photon-photon entanglement dynamics in a bimodal nanocavity, filled with a centrosymmetric nonlinear medium, is studied. In the present study, we have included the first and third order susceptibilities, giving rise to linear and the Kerr-type couplings. With no restrictions placed on the relative strength of these effects, we prove that the corresponding Hamiltonian is block-diagonal, each with ever-growing dimensions. We then show that, depending upon the initial total photon number, one needs to diagonalize a specific low-dimensional block, leading to the time evolution operator. Consequently, the time-evolution of the von Neumann entropy, as a measure of entanglement, is determined. From an analysis of the von Neumann entropy, we show that the entanglement exhibits oscillations, with plateaus, whose characteristics (period, duration, … ) strongly depend upon the strength of third order susceptibility. Moreover, it is shown that the entanglement is enhanced as the linear coupling is increased. The effect of detuning between photon's frequencies is also discussed.