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Physical Review A

Parametric down-conversion for light beams possessing orbital angular momentum

Jochen Arlt, Kishan Dholakia, L. Allen, Miles J. Padgett

Published May 1, 1999• 124 citations
Publisher

Abstract

We investigate the spontaneous parametric down-conversion for light beams possessing orbital angular momentum. The experimental results indicate that the orbital angular momentum is not conserved within the classical light fields. This is in contrast to second harmonic generation where the conservation of orbital angular momentum leads to a well-defined mode transformation. We attribute this difference in behavior to the loss of spatial coherence within each of the down-converted fields.

DOI
10.1103/physreva.59.3950

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We investigate the spontaneous parametric down-conversion for light beams possessing orbital angular momentum. The experimental results indicate that the orbital angular momentum is not conserved within the classical light fields. This is in contrast to second harmonic generation where the conservation of orbital angular momentum leads to a well-defined mode transformation. We attribute this difference in behavior to the loss of spatial coherence within each of the down-converted fields.
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.
We show that the transfer of the plane-wave spectrum of the pump beam to the fourth-order transverse spatial correlation function of the two-photon field generated by spontaneous parametric down-conversion leads to the conservation and entanglement of orbital angular momentum of light. By means of a simple experimental setup based on fourth-order (or two-photon) interferometry, we show that our theoretical model provides a good description for down-converted fields carrying orbital angular momentum.
We study the two-photon detection amplitude of the down-converted beams in spontaneous parametric down-conversion when the physical variable of orbital angular momentum is involved, taking into account both conservation and non-conservation of angular momentum. Agreeing with experimental observations, our theoretical calculation shows that spatial structure of the two-photon detection amplitude of the down-converted beams carries important information about conservation or non-conservation of orbital angular momentum in spontaneous parametric down-conversion.
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.
States of light that are simultaneously eigenstates of orbital, intrinsic, and total angular momentum are found and eigenstates describing pairs of photons from spontaneous parametric down-conversion reveal classes of photon conversion with angular momentum conservation and cases where the initial angular momentum from the pump laser beam is shared between the converted photons and the generating medium. These angular momentum conservation laws open up a wide range of applications to be explored.
Conservation laws are at the heart of our natural scientific understanding, as they dictate why certain phenomena do or do not exist in nature. In the realm of nonlinear optics — where light-matter interactions enable the generation of photon pairs — these principles are also essential. In the common interpretation of spontaneous parametric down-conversion (SPDC), the conservation of momenta is attributed to the transfer of the well-defined linear or orbital angular momenta (OAM) of the single pump photon to the generated photon pair [1], [2]. However, due to the low conversion efficiencies, this conservation rule has only been tested with a strong coherent laser pumping the process. Here, we show for the first time that the OAM of a single pump photon is indeed conserved and that an OAM quanta of up to 2 is transferred to the generated photon pair.