New configurations in parametric down conversion for generating light with orbital angular momentum

The OAM of light provides a new resource to explore quantum physics in a d-dimensional Hubert space, beyond the two dimensional Hubert space generated by the polarization state of the photons. The implementation of such a d-dimensional quantum channel requires the generation of arbitrary engineered entangled states, thus controlling the OAM of the entangled photons is of paramount importance for many applications. Here we address the orbital angular momentum, i.e. the spatial shape, of photons generated in SPDC in non collinear geometries, when the interacting waves can exhibit Poynting vector walk off. The spatial shape depends on the interplay between the state ellipticity caused by the nonlinear geometry, and the Poynting vector walk off. The importance of both effects is dictated by the relationship between three characteristics lengths: the length of the nonlinear crystal, the walk off length and the non collinear length. The effects described here are relevant to current experiments, especially for the implementation of quantum information protocols based on spatially encoded information. Finally, the consideration of new geometries for SPDC, more specifically, highly non collinear configurations, will lead us to the discussion of the relationship between the OAM of the classical beam that pumps the nonlinear crystal, and the quantum OAM of the down converted photons. Regarding experimental measurements related to this issue, it is of great importance to make a clear distinction between the measurement of locally paraxial light beams in a suitable transverse frame, and the description of the global down conversion process, which is not necessarily paraxial.