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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Twisted photons: new classical and quantum applications

Juan P. Torres, Gabriel Molina‐Terriza, Lluís Torner

Published Sep 16, 2005• 16 citations
Publisher

Abstract

Twisted light, or light with orbital angular momentum (OAM), plays an emerging role in both classical and quantum science, with important applications in areas as diverse as biophotonics, micromachines, spintronics, or quantum information. It offers fascinating opportunities for exploring new fundamental ideas in physics, as well as for being used as a tool for practical applications. One important point is to determine how to generate single photons, and two-photon states, with an appropriate OAM content. Here we describe the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric down-conversion (SPDC) in different non-collinear geometries. These geometries introduce a variety of new features. In particular, we find the OAM 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. 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.

DOI
10.1117/12.625393

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Twisted light, or light with orbital angular momentum (OAM), plays an emerging role in both classical and quantum science, with important applications in areas as diverse as biophotonics, micromachines, spintronics, or quantum information. It offers fascinating opportunities for exploring new fundamental ideas in physics, as well as for being used as a tool for practical applications. One important point is to determine how to generate single photons, and two-photon states, with an appropriate OAM content. Here we describe the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric down-conversion (SPDC) in different non-collinear geometries. These geometries introduce a variety of new features. In particular, we find the OAM 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. 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 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.
The OAM of light provides a new resource to explore quantum physics in a d-dimensional Hilbert space, beyond the two dimensional Hilbert space generated by the polarization state of the photons. The implementation of such a ddimensional quantum channel requires the generation of arbitrary engineered entangled states, thus controlling the OAM of the entangled photons is of paramount importance for many applications. Here we address the orbital angular momentum, i.e. the spatial shape, of photons generated in SPDC in non collinear geometries, when the interacting waves can exhibit Poynting vector walk off. The spatial shape depends on the interplay between the state ellipticity caused by the nonlinear geometry, and the Poynting vector walk off. The importance of both effects is dictated by the relationship between three characteristics lengths: the length of the nonlinear crystal, the walk off length and the non collinear length. The effects described here are relevant to current experiments, especially for the implementation of quantum information protocols based on spatially encoded information. Finally, the consideration of new geometries for SPDC, more specifically, highly non collinear configurations, will lead us to the discussion of the relationship between the OAM of the classical beam that pumps the nonlinear crystal, and the quantum OAM of the down converted photons. Regarding experimental measurements related to this issue, it is of great importance to make a clear distinction between the measurement of locally paraxial light beams in a suitable transverse frame, and the description of the global down conversion process, which is not necessarily paraxial.
Angular momentum plays an iniport,aiit role in both classical and quantum physics. Historically the angular momentum content of a photon was divided into spin or polarization angular momentum (PAM), which relies in the vectorial structure of the field, and orbital angular momentum (OAM), which is usually related with the spatial structure of the beam. It has been experimeiitally demonstrated that, under the paraxial approximation, one can manipulate independently the PAM and the OAM. While the former is a classical tool in quantum information experiments, only recently the potential of the OAM has been explored. In particular, it was demonstrated recently that the idler and signal photons produced in the process of spontaneous parametxic downconversion constitute an entangled state of OAM [l]. The experiment showed that when the beam that pumps the nonlinear crystal is an eigenstate of the OAM, the quantum state of the down converted photons can in principle be described as IQ
The generation of paired photons entangled in orbital angular momentum (OAM), provides a new degree of freedom that is increasingly being used as a source of quantum states. Elucidation of the OAM spectrum of OAM spectrum of the generated photons is of paramount importance, since quantum information applications require the ability to generate arbitrary entangled states with the appropriate OAM correlations. Here we discuss the OAM spectrum of the photon generated via SPDC in two complementary scenarios. On one hand, we should consider the whole geometry of the nonlinear process, taking into account azimuthal variations of the nonlinear coefficient or the phase matching conditions. On the other hand, all relevant experiments reported to date detect only a small section of the full down-conversion cone. In this scenario, the measured OAM correlations depend of the emission angle of the photons and the strength of the Poynting vector walk-off. We will present experiments in SPDC where this dependence is clearly revealed.