2. Non-separable beam generation

The previous experiment produces two squeezed modes with orthogonal polarizations, meaning that quantum correlations have been created between other polarization modes during the interaction with the atoms. We developed a general method to figure out the maximally entangled modes in the sense of the inseparability criterion for continuous variables recently derived by Duan et al. [1].

Using two homodyne detections, we have shown that the modes polarized at 45° with respect to the main linear polarizations are maximally entangled, and we have measured directly the "quadrature entanglement" of the beam exiting the cavity [2].

In a complementary experiment, we have mixed this beam with an intense coherent beam on a polarizing beamsplitter and obtained two spatially separated beams. By locking the intense beam phase with that of the entangled beam, we have mapped its entanglement onto a polarization basis, thus achieving "polarization entanglement" (i.e. entanglement between two pairs of Stokes operators [3]).

[1] L.M. Duan, G. Giedke, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 84, 2722 (2000) [quant-ph/9909044]

[2] V. Josse, A. Dantan, A. Bramati, M. Pinard, E. Giacobino [quant-ph/0306147]

[3] N. Korolkova, G. Leuchs, R. Loudon, T.C. Ralph, C. Silberhorn, Phys. Rev. A 65, 052306 (2003) [quant-ph/0108098]