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arXiv:2007.03883 · Physical Review A

Transfer of angular spectrum in parametric down-conversion with structured light

Antonio Zelaquett Khoury, P. H. Souto Ribeiro, K. Dechoum

Published Sep 8, 2020• 13 citations
arXivHTMLPDF

Abstract

We develop the formal approach to the angular spectrum transfer in parametric down-conversion that allows pumping with a structured beam. The scheme is based on an entangled photon source pumped by a laser beam structured with a vector-vortex polarization profile. This creates a two-photon quantum state exhibiting polarization-dependent transverse correlations that can be accessed through coincidence measurements on the spatially separated photons. The calculated correlations are shown to present a spin-orbit profile typical of vector beams, however, distributed on separate measurement regions. Our approach allows the design of the pump beam vector spatial structure and measurement strategies for potential applications of these entangled states, such as in quantum communication.

DOI
10.1103/physreva.102.033708

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We develop the formal approach to the angular spectrum transfer in parametric down-conversion that allows pumping with a structured beam. The scheme is based on an entangled photon source pumped by a laser beam structured with a vector-vortex polarization profile. This creates a two-photon quantum state exhibiting polarization-dependent transverse correlations that can be accessed through coincidence measurements on the spatially separated photons. The calculated correlations are shown to present a spin-orbit profile typical of vector beams, however, distributed on separate measurement regions. Our approach allows the design of the pump beam vector spatial structure and measurement strategies for potential applications of these entangled states, such as in quantum communication.
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.
In this article we investigate the orbital angular momentum spectrum of photons produced in parametric down conversion process. We study how the transverse profile of the pump mode affects the spectrum as compared to a gaussian pump beam. We show that using perfect optical vortex mode as pump the spectrum can be highly narrowed down. We further study the entanglement between the two down converted photons in the orbital angular momentum basis. We observe that photons entangled in Laguerre-Gaussian modes exhibit greater higher dimensional entanglement.
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.
Stimulated parametric down-conversion (StimPDC) is the seeded version of the process that underlies much of photonic quantum information. Replacing the vacuum at one input port with a coherent seed leaves the interaction Hamiltonian, the phase-matching function and the two-photon amplitude unchanged, while raising the output to levels accessible with ordinary classical detectors. This review treats the transverse spatial physics of that process. We show that a single relation, in which the idler amplitude is the pointwise product of the pump field with the complex conjugate of the seed, organizes results usually presented separately: the image and coherence transfer experiments of the 1990s; phase conjugation and its use for wavefront correction; the conservation and conjugation of orbital angular momentum, together with the generation of radial modes and geometric intensity patterns; and the processing of vector vortex beams carrying spatially varying polarization. We then consider StimPDC as an instrument rather than as an object of study, covering stimulated emission tomography, the experimental realization of Klyshko's advanced-wave picture, and the transfer of partial coherence, including the conservation of the twist phase of twisted Gaussian Schell-model beams. We close with the quantum regime, reached when the seed approaches the single-photon level or the idler is used as a herald, and with an assessment of open problems and prospective applications.
A vector vortex beam presents local polarization states that are spatially modulated in the plane transverse to propagation. By employing a two-crystal-sandwich source allowing for nonlinear interactions between input fields of any polarization, we analyze experimentally the process of stimulated parametric down-conversion and observe unique effects when the pump and seed fields are vector vortex beams. We reconstruct the transverse polarization pattern of the generated idler beam by Stokes polarimetry. The experimental results obtained are in good qualitative agreement with theory and exhibit manifold polarization transverse distributions for different combinations of pump and seed vector vortex beams, which may find applications in both classical and quantum optics.
Hybrid entangled states, having entanglement between different degrees-of-freedom (DoF) of a particle pair, are of great interest for quantum information science and communication protocols. Among different DoFs, the hybrid entangled states encoded with polarization and orbital angular momentum (OAM) allow the generation of qubit-qudit entangled states, macroscopic entanglement with very high quanta of OAM and improvement in angular resolution in remote sensing. Till date, such hybrid entangled states are generated by using a high-fidelity polarization entangled state and subsequent imprinting of chosen amount of OAM using suitable mode converters such as spatial light modulator in complicated experimental schemes. Given that the entangled sources have feeble number of photons, loss of photons during imprinting of OAM using diffractive optical elements limits the use of such hybrid state for practical applications. Here we report, on a simple experimental scheme to generate hybrid entangled state in polarization and OAM through direct transfer of classical non-separable state of the pump beam in parametric down conversion process. As a proof of principle, using local non-separable pump state of OAM mode l=3, we have produced quantum hybrid entangled state with entanglement witness parameter of W-1.25 violating by 8 standard deviation. The generic scheme can be used to produce hybrid entangled state between two photons differing by any quantum number through proper choice of non-separable state of the pump beam.