Theory of quantum entanglement of intra-cavity photons produced by a non-degenerate parametric oscillator (NDPO); Semi-classical approach

Abstract

The von-Neumann entropy (VNE) which is usually expressed in terms of the density operator is the mathematical tool to measure the degree of entanglement of a bi-partite system. Applying the solutions of the quantum Langevin equations, the anti-normally ordered characteristic function of the intra-cavity photons produced by a non-degenerate parametric oscillator is calculated. With the help of the resulting characteristic function, the Q function which is then used to calculate the entanglement of the intra-cavity photons using VNE is determined. Moreover, the photon number distribution of the intra-cavity photons produced by a non-degenerate parametric oscillator coupled to a two-mode squeezed vacuum reservoir is determined.