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Optics Letters

Orbital angular momentum of entangled counterpropagating photons

Juan P. Torres, Clara I. Osorio, Lluís Torner

Published Aug 13, 2004• 39 citations
Publisher

Abstract

We elucidate the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric downconversion in different noncollinear geometries in which the entangled photons counterpropagate. We find, in particular, the orbital angular momentum of entangled pairs generated in transverse-emitting configurations, in which none of the known rules for selecting orbital angular momentum holds.

DOI
10.1364/ol.29.001939

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We elucidate the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric downconversion in different noncollinear geometries in which the entangled photons counterpropagate. We find, in particular, the orbital angular momentum of entangled pairs generated in transverse-emitting configurations, in which none of the known rules for selecting orbital angular momentum holds.
We elucidate the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric down-conversion (SPDC) in different non-collinear geometries. To date, most investigations addressed SPDC in nearly collinear phase-matching geometries, where the pump, the signal and idler photons propagate coaxially almost along the same direction. However, non-collinear geometries introduce a variety of new features. The OAM of the entangled photons strongly depend on the propagation direction of the photons. Here we show that locally paraxial measurements of the OAM conducted with entangled photons generated in non collinear geometries, they do not comply with the known selection rules for the spiral index of the pump, signal and idler mode functions (Mair et al., Nature 412, 313 (2001)). In particular, we find the orbital angular momentum of entangled pairs generated in purely transverse-emitting configurations, where the entangled photons counter-propagate perpendicularly to the direction of propagation of the pump beam. In transverse emitting configurations, the spatial shape of the down converted in one transverse dimensions strongly depends on the corresponding spatial shape of the input pump beam, while in the other transverse dimension, the shape is tailored by the longitudinal phase matching. The spatial walk-off of all interacting waves in the parametric process also determines the OAM content of the down-converted photons, and here its influence is also revealed.
We show that the orbital angular momentum (OAM) correlations, and the amount of spatial entanglement, of paired photons generated in spontaneous parametric downconver- sion are strongly affected by the use of noncollinear configurations and by the presence of Poynting vector walk-off. We discuss how our results are related to the question of the conservation of OAM in a nonlinear optics process, and we derive selection rules that allow to determine the sought-after OAM correlations, especially for those configurations used in current quantum information experiments.
The generation of paired photons entangled in the spatial degree of freedom, i.e., in orbital angular momentum, offers a convenient physical resource to investigate the nature of entanglement in a multidimensional Hilbert space with controllable dimensionality. The two main physical processes that generate pairs of photons which show correlations in orbital angular momentum are (a) spontaneous parametric down-conversion (SPDC), and (b) Raman transitions induced in atomic ensembles. One question naturally arises: what kinds of correlations exist between the orbital angular momentum of the generated photons? The answer might be different if we consider the whole quantum state of the generated photons, i.e., all possible directions where the pairs of photons can be emitted, or if we consider only a small section of the full set of directions.