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Journal of Optics B Quantum and Semiclassical Optics

The orbital angular momentum of down-converted photons

Xi‐Feng Ren, Guo‐Ping Guo, Bo Hao Yu, Jian Li, Guang‐Can Guo

Published Mar 26, 2004• 31 citations
Publisher

Abstract

We calculate the relative amplitude of the orbital angular momentum (OAM) of entangled photon pairs from the spontaneous parametric down-conversion of a thin quadratic nonlinear crystal. The results show that the amplitude depends on both of the two Laguerre indices l , p . We also discuss the influences of the commonly used holograms and mono-mode fibres for mode analysis. We conclude that only a few dimensions can be explored from the infinite OAM modes of down-converted photon pairs.

DOI
10.1088/1464-4266/6/4/008

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We calculate the relative amplitude of the orbital angular momentum (OAM) of entangled photon pairs from the spontaneous parametric down-conversion of a thin quadratic nonlinear crystal. The results show that the amplitude depends on both of the two Laguerre indices l , p . We also discuss the influences of the commonly used holograms and mono-mode fibres for mode analysis. We conclude that only a few dimensions can be explored from the infinite OAM modes of down-converted photon pairs.
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.
Abstract In this work, we investigate the orbital angular momentum (OAM) spectrum of photons generated via spontaneous parametric down-conversion (SPDC) and study how shaping the transverse profile of the pump beam influences the resulting spectrum. Using a perfect optical vortex (POV) mode as the pump, we show that the OAM spectrum narrows significantly, leading to purer OAM states. We further examine the entanglement between the down-converted photons in the OAM basis, finding that Laguerre–Gaussian (LG) pumped photons exhibit increased higher-dimensional entanglement at the expense of mode purity.
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 bandwidth of any communication system, classical or quantum, is limited by the number of orthogonal states in which the information can be encoded. Quantum key distribution systems available commercially rely on the two-dimensional polarisation state of photons. Quantum computation has also been largely designed on the basis of qubits. However, a photon is endowed with other degrees of freedom, such as orbital angular momentum (OAM). OAM is an attractive basis to be used for quantum information because it is discrete and theoretically infinite-dimensional. This promises a higher information capacity per photon which can lead to more complex quantum computation protocols and more security and robustness for quantum cryptography. Entanglement of OAM naturally arises from spontaneous parametric down-conversion (SPDC). However, any practical experiment utilising the innately high-dimensional entanglement of the orbital angular momentum (OAM) state space of photons is subject to the modal capacity of the detection system. Only a finite subset of this space is accessible experimentally. Given such a constraint, we show that the number of measured, entangled OAM modes in photon pairs generated by SPDC can be increased by tuning the phase-matching conditions in the SPDC process. We achieve this by tuning the orientation angle of the nonlinear crystal generating the entangled photons.