Effects of medium characteristics on the properties of thermal photon-photon entanglement in a nonlinear nanocavity

In this paper we study the properties of photon-photon thermal entanglement occurring in a nonlinear optical cavity. The photons are thermally produced inside a nonlinear cavity that couples the two modes via first and third order susceptibilities. Diagonalizing the Hamiltonian of the system, the thermal density matrix and, consequently, the partially transposed one are obtained. The negative eigenvalues of the latter are then calculated, leading to the negativity as a measure of photon-photon entanglement. Our results show that the two photons are separable at absolute zero. As the temperature increases, the negativity exhibits a maximum whose value strongly depends on the medium characteristics and then asymptotically vanishes.