Interference and complementarity for two-photon hybrid entangled states

In this work we generate two-photon hybrid entangled states (HESs), where the polarization of one photon is entangled with the transverse spatial degree of freedom of the second photon. The photon pair is created by parametric down-conversion in a polarization-entangled state. A birefringent double-slit couples the polarization and spatial degrees of freedom of these photons, and finally, suitable spatial and polarization projections generate the HES. We investigate some interesting aspects of the two-photon hybrid interference and present this study in the context of the complementarity relation that exists between the visibility of the one-photon and that of the two-photon interference patterns.