Effect of temperature on 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 cavity is in thermal equilibrium with a reservoir at a temperature T, so that the bimodal photonic states are determined by the Boltzmann factor. The nonlinear cavity couples the two modes via first and third order susceptibilities. The structure of the total Hamiltonian enables us to develop a computational scheme for determining the energy eigenstates and eigenvalues. Consequently, the thermal density matrix, the negative eigenvalues of the partially transposed one and, thereby, the negativity, as a measure of photon-photon free entanglement, are computed. Our results show that the negativity vanishes at absolute zero, indicating that the ground state is separable. As the temperature increases, the negativity exhibits a maximum, at a certain temperature, and then asymptotically vanishes. Moreover, we demonstrate how the maximal entanglement as well as the temperature at which it occurs, is characterized by the properties of the medium. The roles of nonlinearities on such characteristics are also discussed in detail.