Imaging symmetric and antisymmetric behavior of orbital-angular-momentum-entangled two-photon states

We report on an experiment in which orbital-angular-momentum (OAM)-entangled photon pairs generated by the spontaneous parametric down-conversion process can be engineered to have particular symmetry properties. Our method is based on the use of a Dove-prism pair in conjunction with Hong-Ou-Mandel (HOM) interferometry resolved in transverse position and OAM. The latter allows us to engineer the postselected two-photon state to exhibit a specific type of symmetry. By selecting particular topological charge values for the pump and for the postselected two-photon state, we can transition from a symmetric two-photon state and a HOM dip to an antisymmetric state and a HOM peak. Spatial resolution allows us to obtain the HOM interferogram both at the single-pixel level and globally by summing over all sensor pixels. Furthermore, through spatially selective OAM projection of the detected photon pairs, we can define multiple transverse regions with different symmetry properties, as verified by our spatially resolved HOM apparatus. Although we used two transverse regions for this proof-of-concept demonstration, this method could in principle be scaled to a larger number of regions, leading to a new technique to be added to the existing toolbox for quantum technologies in the photonic domain.