Entanglement of the l- and the r-photons in an anisotropic crystal

Light incident onto an anisotropic crystal is divided into the ordinary and the extraordinary waves which vibrate in two perpendicular directions. Because of the tensor property of the dielectric constant, the direction of the electric displacement is not parallel to the vector of the incident electric field. An optical torque is induced by incidence of the linearly polarized light and propagating through the crystal. The optical torque tends to rotate the directions of eigenvibration which results in self-modulation of the ordinary and the extraordinary waves, and causes an energy splitting of the left (l)-, and the right (r)-handed circularly polarized waves in the crystal. The l- and the r-photons are correlated through the optical torque, which are found to be in an entanglement state.