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Physical Review Letters

Orbital and Intrinsic Angular Momentum of Single Photons and Entangled Pairs of Photons Generated by Parametric Down-Conversion

H. H. Arnaut, G. A. Barbosa

Published Jul 10, 2000• 245 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.85.286

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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.
A recent work [H. H. Arnaut and G. A. Barbosa, Phys. Rev. Lett. 85, 286 (2000)] has shown eigenstates describing pairs of photons from spontaneous parametric down-conversion, which are eigenstates of orbital, intrinsic, and total momentum. Experimental demonstration of transfer of angular momentum to parametric down-converted photons has also been achieved [A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001)]. This work shows conditions for phase matching and examples are given for a Laguerre-mode pump beam. Polar and azimuthal angles are connected by phase matching giving a peculiar divergence pattern for the down-converted light. Full entanglement of polarization and angular-momentum states of photons is discussed.
Identifying conservation laws is central to every subfield of physics, as they illuminate the underlying symmetries and fundamental principles. A prime example can be found in quantum optics: the conservation of orbital angular momentum (OAM) during spontaneous parametric down-conversion (SPDC) enables the generation of a photon pair with entangled OAM. In this Letter, we report on the observation of OAM conservation in SPDC pumped on the single-photon level by a preceding SPDC process. We implement this cascaded down-conversion scheme in free space, without waveguide confinement, and thereby set the stage for experiments on the direct generation of multiphoton high-dimensional entanglement using all degrees of freedom of light.
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.
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.