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Verification of hologram position in experiment of entanglement in orbital angular momentum of photons

Orbital angular momentum of photons is one of the variables of physical systems that can be used to realize multi-dimensional quantum entanglement. LG mode has ring like intensity distribution and helical phase front. A single photon in LGm mode has orbital angular momentum m η . Recently, Zeilinger group reported that photon pairs generated in parametric down conversion share entanglement in orbital angular momentum [1]. In these experiments, a hologram (with a dislocation point) is used to convert orbital angular momentum, making basis identification difficult. The main reason is that we cannot know the position of the hologram’s dislocation point respective to beam center position. To measure hologram position, our method is to compare calculated coincidence probability distribution with coincidence counts distribution obtained experimentally using photon pairs. Experimental setup is shown in FIG.1. A CW argon laser (351.1nm, LG0 mode) was used to pump a nonlinear crystal (BBO, Type-I phase matching condition). Photon pairs were analyzed in LG mode basis using hologram, single-mode fiber and a photon detector in each path A and B. Hologram position of optical path B is unknown. To estimate hologram B’s position, we measured coincidence counts of photon pairs scanning hologram A position 2-dimensionaly. The result is a coincidence counts 2D map shown in FIG.2 (left side). The observed distribution is not symmetric about the rotation around the origin. It suggest that a photon in path A being a superposition states of LG modes with a particular phase detected, when the corresponding photon is detected in path B. With some assumptions, we can derive coincidence probability distribution,