Exploiting SPDC of photons in polarization singular modes to generate heralded-single photons in remotely controlled topological classes

\nPolarization structured heralded single photons have been generated through spontaneous parametric down-conversion in a type-I dual crystal pumped by an inhomogeneously polarized beam in a general Poincaré mode, i.e. an inseparable superposition of two orthogonally polarized states through two orthogonal orbital angular momentum modes. The polarization structure of the signal photons can be controlled by manipulating the polarization state of their idler photon sisters with zero orbital angular. Due to the separate conservations of spin and orbital angular momenta in a type-I dual crystal SPDC process, any projection of the idler polarization state turns into a unitary transformation of the polarization basis of the signal photons, while preserving the orbital angular momentum modes originally included in the pump. We demonstrate, in this way, the ability to toggle between direct and basis-switched pump-single photon transfer by selectively projecting the polarization of the heralding photon before detection.\n