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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Transverse structures in spontaneous parametric down-conversion with orbital angular momentum

Geraldo A. Barbosa, Prem Kumar

Published Jan 1, 2007• 0 citations
Publisher

Abstract

Coincidence structures carrying orbital angular momentum in Type-II spontaneous- parametric-down-conversion are obtained theoretically. Azimuthal symmetry breaking around the pump beam direction is reflected on these structures.
DOI
10.1364/cqo.2007.csua2

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arXiv:quant-ph/0703212•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 12, 2007•0 citations
Several wave-function approximations describing spontaneous parametric down-conversion can be found in the literature. Basically all cases are derived from the standard Hamiltonian for parametric down-conversion. Most frequently, particular cases describing collinear or paraxial approximations are described. This work presents a wave function in compact form, valid for all cases of single photon-pair conversion (Type I or Type II), for all angles allowed by the phase-matching conditions and for all orbital angular momentum values lll. Examples are given of coincidence structures to be expected for signal and idler photons. Partial transfer of orbital angular momentum from the pump laser to the photon pair is discussed. Some hypothesis for the decay channels of the nontransferred part of the orbital angular momentum is made.
Directly contradictory arguments coexist regarding the conservation rule of orbital angular momentum in spontaneous parametric down-conversion. We analytically show how this rule is decided by spatial symmetry. We discover that the down-converted photon pairs can carry non-negligible extrinsic orbital angular momentum in the degrees of relative-movement freedom due to spatial symmetry breaking, leading to nonconservation of total orbital angular momentum in type-II down-conversion. Also, we demonstrate that the traditional technique does not measure the extrinsic orbital angular momentum.
Experimental observation of the conservation of orbital angular momentum in spontaneous parametric down-conversion has been theoretically attributed to phase-matching, transfer of plane-wave spectrum from pump beam to down-converted beams. However, according to quantum mechanics, the conservation of angular momentum arises from rotational symmetry of the Hamiltonian describing the studied physical process. Recently, experimental evidence has been found which shows that non-conservation of orbital angular momentum can occur in spontaneous parametric down-conversion due to rotational asymmetry of the Hamiltonian. In this paper, we theoretically show that all reported experimental results of conservation of orbital angular momentum in spontaneous parametric down-conversion are determined only by the Hamiltonian symmetry, and not by phase matching, transfer of plane-wave spectrum.