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), 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 could be calculated. With the help of the resulting characteristic function, the Q- function which is then used to calculate the entanglement of the intracavity photons using VNE is determined. Moreover, the photon number distribution, the mean photon number, the normalized second order correlation function, the intensity difference, and quadrature variance for the intra-cavity photons produced by a nondegenerate parametric oscillator coupled to a two-mode squeezed vacuum reservoir is determined. It was found that when the squeeze parameter increases the entanglement also increases. These show that the entropy entanglement has a direct relation with squeezing.

Keywords:Entanglement, Mean photon number, Parametric down conversion, Q-function