Entanglement of the transverse degrees of freedom of the photon

Using two parametric down-converters, it is possible to prepare twin photons in position-entangled states, where the photons are labelled by their birth position. We have measured the interference between the two probability amplitudes for a twin-photon pair: of being born in the first crystal or in the second one. The oscillation frequency of the coincidence pattern can be varied through independent phase differences in the signal and idler beams. Entangled states in position and also in the polarization sub-space can be prepared with this source. In this case, measurement of the position interference can give us information about the degree of polarization entanglement.