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arXiv:2108.01759 · Physical Review A

Biphoton phase-space correlations from Gouy-phase measurements using double slits

F. C. V. de Brito, I. G. da Paz, Jonas B. Araujo, Marcos Sampaio

Published Dec 17, 2021• 2 citations
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Abstract

Quantum correlations encoded in photonic Laguerre-Gaussian modes were shown to be related to the Gouy-phase shifts [Kawase et al., Phys. Rev. Lett. 101, 050501 (2008)], allowing for a nondestructive manipulation of photonic quantum states. In this work, we exploit the relation between phase-space correlations of biphotons produced by spontaneously parametric down-conversion (SPDC) as encoded in the logarithmic negativity (LN) and the Gouy phase as they are diffracted through an asymmetrical double-slit setup. Using an analytical approach based on a double-Gaussian approximation for type-I SPDC biphotons, we show that measurements of Gouy-phase differences provide information on their phase-space entanglement variation, governed by the physical parameters of the experiment and expressed by the LN via covariance matrix elements.

DOI
10.1103/physreva.104.062430

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Quantum correlations encoded in photonic Laguerre-Gaussian modes were shown to be related to the Gouy-phase shifts [Kawase et al., Phys. Rev. Lett. 101, 050501 (2008)], allowing for a nondestructive manipulation of photonic quantum states. In this work, we exploit the relation between phase-space correlations of biphotons produced by spontaneously parametric down-conversion (SPDC) as encoded in the logarithmic negativity (LN) and the Gouy phase as they are diffracted through an asymmetrical double-slit setup. Using an analytical approach based on a double-Gaussian approximation for type-I SPDC biphotons, we show that measurements of Gouy-phase differences provide information on their phase-space entanglement variation, governed by the physical parameters of the experiment and expressed by the LN via covariance matrix elements.
We propose experimental measurements of the logarithmic negativity, which quantifies quantum correlations using Gouy phase measurements in an asymmetric double-slit interference experiment for twin photons. This is possible because both quantities have analogous dependence with the spatial confinement by the slits and enables one to manipulate the portion of entanglement by the Gouy phase. In order to obtain those measurements, we need to work in a regime where the position correlations between particles are strong, therefore we investigate such correlations for biphotons. Since we would like to handle entanglement quantifiers through the Gouy phase, we analyze the Gouy phase difference for two entangled photons in an asymmetric double-slit interference experiment.
Spontaneous parametric down-conversion (SPDC) is a widely used source for photonic entanglement. Years of focused research have led to a solid understanding of the process, but a cohesive analytical description of the paraxial biphoton state has yet to be achieved. We derive a general expression for the spatio-temporal biphoton state that applies universally across common experimental settings and correctly describes the nonseparability of spatial and spectral modes. We formulate a criterion on how to decrease the coupling of the spatial from the spectral degree of freedom by taking into account the Gouy phase of interacting beams. This work provides new insights into the role of the Gouy phase in SPDC, and also into the preparation of engineered entangled states for multidimensional quantum information processing.
Abstract We experimentally demonstrate the quantum entanglement in various spatial modes of the correlated photons generated via spontaneous parametric down-conversion in a type-II phase-matched periodically-poled KTP crystal. The two-fold coincidence measurement reveals the spatial entanglement between the photon pairs by projecting one of the correlated photons onto a Gaussian mode while scanning the spatial mode of its partner photon through selective projection (Gaussian, Laguerre–Gaussian (LG), Bessel-Gaussian (BG), and Airy–Gaussian (AG)) using a spatial light modulator (SLM). We also show the spatially resolved measurement of the non-conservation of orbital angular momentum via modal decomposition of the correlated photon in LG and BG bases.
High-dimensional spatial entanglement generated via spontaneous parametric down-conversion (SPDC) provides a powerful resource for quantum information processing, yet its mode structure becomes increasingly complex when the pump occupies a higher-order Laguerre--Gaussian (LG) mode. Here, we develop an algebraic framework for characterizing biphoton spatial-mode entanglement by factorizing LG-pumped SPDC into a spatial-mode beam-splitter transformation followed by spatial two-mode squeezing. By choosing the biphoton LG basis radius as the geometric mean of the pump-beam radius and the crystal-induced correlation width, we obtain a natural modal basis in which the two operations can be treated separately. When the pump-beam radius matches the correlation width, spatial squeezing vanishes, and the two circular-mode components of the pump are independently conserved across the signal and idler photons, leading to conservation of both orbital angular momentum and the total spatial mode number. We further derive an analytical expression for the Schmidt number for arbitrary LG pump modes and squeezing strengths, revealing how the radial and azimuthal pump indices govern the dimensionality of the spatial entanglement. This algebraic characterization provides a unified description of the mode structure, conservation laws, and entanglement dimensionality of higher-order-LG-pumped SPDC.