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 caesium atoms placed in an optical cavity. We convert the squeezing of the two linear polarization modes into quadrature entanglement and show how to find the best entanglement generated in a two-mode system using the inseparability criterion for continuous variables (Duan et al 2000 Phys. Rev. Lett. 84 2722). We verify this method experimentally with a direct measurement of the inseparability using two homodyne detectors. We then map this entanglement into a polarization basis and achieve polarization entanglement