Twin photons with angular-momentum entanglement: Phase matching

Abstract

A recent work [H. H. Arnaut and G. A. Barbosa, Phys. Rev. Lett. 85, 286 (2000)] has shown eigenstates describing pairs of photons from spontaneous parametric down-conversion, which are eigenstates of orbital, intrinsic, and total momentum. Experimental demonstration of transfer of angular momentum to parametric down-converted photons has also been achieved [A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001)]. This work shows conditions for phase matching and examples are given for a Laguerre-mode pump beam. Polar and azimuthal angles are connected by phase matching giving a peculiar divergence pattern for the down-converted light. Full entanglement of polarization and angular-momentum states of photons is discussed.