Entanglement and squeezing in a two-mode system: theory and experiment

We report on the generation of non separable beams produced via the interaction of a linearly polarized beam with a cloud of cold cesium atoms placed in an optical cavity. We convert the squeezing of the two linear polarization modes into quadrature entanglement and show how to find out the best entanglement generated in a two-mode system using the inseparability criterion for continuous variable [Duan et al., Phys. Rev. Lett. 84, 2722 (2000)]. We verify this method experimentally with a direct measurement of the inseparability using two homodyne detections. We then map this entanglement into a polarization basis and achieve polarization entanglement.Comment: submitted to J. Opt. B for a Special Issue on Foundations of Quantum Optic