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Optics & Laser Technology

Tailoring orbital angular momentum entanglement through inverse design based on gradient descent

Youngbin Na, Do‐Kyeong Ko

Published Jun 9, 2025• 1 citation
Publisher

Abstract

High-dimensional quantum entanglement is an important resource for fundamental research and quantum technological application. Recently, the orbital angular momentum (OAM) of light has received much attention to realize high-dimensional quantum systems, and generating and manipulating the OAM entanglement has become an important topic. Here, we propose an inverse design technique to manipulate the OAM entanglement of the photon pair generated through spontaneous parametric down-conversion. The proposed technique directly tailors the OAM states of entangled photon pairs by shaping the incident pump beam. In particular, we construct a physics-informed model by leveraging the backpropagation algorithm and adhering to the overlap integral relation. Our model automatically optimizes diffractive masks, allowing the structured pump to quantitatively modulate the OAM distribution. The generation of maximally entangled states in different dimensions is demonstrated numerically and experimentally.

DOI
10.1016/j.optlastec.2025.113283

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High-dimensional quantum entanglement is an important resource for fundamental research and quantum technological application. Recently, the orbital angular momentum (OAM) of light has received much attention to realize high-dimensional quantum systems, and generating and manipulating the OAM entanglement has become an important topic. Here, we propose an inverse design technique to manipulate the OAM entanglement of the photon pair generated through spontaneous parametric down-conversion. The proposed technique directly tailors the OAM states of entangled photon pairs by shaping the incident pump beam. In particular, we construct a physics-informed model by leveraging the backpropagation algorithm and adhering to the overlap integral relation. Our model automatically optimizes diffractive masks, allowing the structured pump to quantitatively modulate the OAM distribution. The generation of maximally entangled states in different dimensions is demonstrated numerically and experimentally.
An important problem in the practical application of high-dimensional two-photon orbital angular momentum (OAM) entanglement generated by spontaneous down conversion is a lower degree of entanglement, where the amplitudes of modes are not uniformly distributed. In contrast to the previously raised entanglement concentration protocol, we here report on an experimental scheme that addresses this problem by tuning the two-photon quantum angular position correlation. An opaque mask with N evenly distributed angular slits having a radius r is inserted in the two-photon down-conversion light path. The number N should be such that the separation of adjacent angular slits is larger than the scale of the two-photon angular position correlation. The OAM entanglement for the two-photon state after the opaque mask is cast into a set of folded subbands with a dimension of N, owing to the reduction of rotational symmetry from continuous invariance to discrete invariance. Almost maximum OAM entanglement can be realized by properly setting the width of the angular slits.
ENGLISH ABSTRACT: High-dimensional quantum entanglement offers an increase in information capacity per photon; a highly desirable property for quantum information processes such as quantum communication, computation and teleportation. As the orbital angular momentum (OAM) modes of light span an infinite-dimensional Hilbert space, they have become frontrunners in achieving entanglement in higher dimensions. In light of this, we investigate the potential of OAM entanglement of photons by controlling the parameters in both the generation and measurement systems. We show the experimental procedures and apparatus involved in generating and measuring entangled photons in two-dimensions. We verify important quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle correlations, as well as a violation of a Bell-type inequality. By performing a full state tomography, we characterise our quantum state and show we have a pure, highly entangled quantum state. We demonstrate that this method can be extended to higher dimensions. The experimental techniques used to generate and measure OAM entanglement place an upper bound on the number of accessible OAM modes. As such, we investigate new methods in which to increase the spiral bandwidth of our generated quantum state. We alter the shape of the pump beam in spontaneous parametric down-conversion and demonstrate an effect on both OAM and angle correlations. We also made changes to the measurement scheme by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate entanglement in this basis. We show that this method allows the measured spiral bandwidth to be optimised by simply varying the continuous radial parameter of the BG modes. We demonstrate that BG modes can be entangled in higher dimensions compared with the commonly used helical modes by calculating and comparing the linear entropy and fidelity for both modes. We also show that quantum entanglement can be accurately simulated using classical light using back-projection, which allows the study of projective measurements and predicts the strength of the coincidence correlations in an entanglement experiment. Finally, we make use of each of the techniques to demonstrate the effect of a perturbation on OAM entanglement measured in the BG basis. We investigate the self-healing property of BG beams and show that the classical property is translated to the quantum regime. By calculating the concurrence, we see that measured entanglement recovers after encountering an obstruction.
Photon pairs entangled in high-dimensional orbital angular momentum (OAM) degrees of freedom (DOF) have been widely regarded as a possible source for improving the capacity of quantum information processing. The generation of a high-dimensional maximally entangled state in the OAM DOF is therefore much desired. In this work, we demonstrate a simple method to generate a broader and flatter OAM spectrum, i.e., a larger spiral bandwidth (SB), of entangled photon pairs generated through spontaneous parametric down-conversion by modifying the pump beam profile. By investigating both experimentally and theoretically, we find that an exponential pump profile that is roughly the inverse of the mode profiles of the single-mode fibers used for OAM detection will provide a much larger SB compared to a Gaussian-shaped pump.
We propose a method for generation of entangled photonic states in high dimensions, the so-called qudits, by exploiting quantum correlations of Orbital Angular Momentum (OAM) entangled photons, produced via Spontaneous Parametric Down Conversion. Diffraction masks containing N angular slits placed in the path of twin photons define a qudit space of dimension N2, spanned by the alternative pathways of OAM-entangled photons. We quantify the high-dimensional entanglement of path-entangled photons by the Concurrence, using an analytic expression valid for pure states. We report numerical results for the Concurrence as a function of the angular aperture size for the case of high-dimensional OAM entanglement and for the case of high-dimensional path entanglement, produced by N × M angular slits. Our results provide additional means for preparation and characterization of entangled quantum states in high-dimensions, a fundamental resource for quantum simulation and quantum information protocols.
Any practical experiment utilizing the innate DDD-dimensional entanglement of the orbital angular momentum (OAM) of photons is subject to the generation capacity of the entangled photon source and the modal capacity of the detection system. We report an experimental spontaneous parametric-down-conversion system able to generate and detect tunable high-dimensional OAM entanglement. By tuning the phase matching, we demonstrate a factor of 2 increase on the half-width of the OAM-correlation spectrum, from 10 to 20. In terms of quantum mutual information capacity, this is an increase from 3.183.183.18 to 4.954.954.95 bits/photon. Furthermore, we measure correlations in the conjugate variable, angular position, and obtain concurrence values 0.960.960.96 and 0.900.900.90. The good entanglement measures in both OAM and angular position bases indicate bipartite, DDD-dimensional entanglement where DDD is tunable.
Photon pairs generated from spontaneous parametric down-conversion are a well-established method to realize entangled bipartite photonic systems. Laguerre-Gaussian modes, which carry orbital angular momentum (OAM), are commonly exploited to engineer high-dimensional entangled quantum states. For Hilbert spaces with dimension d>2d>2d>2, maximally entangled states (MESs) help to improve the capacity and security of quantum communication protocols, among several other promising features. However, the direct generation of MESs in well-defined high-dimensional subspaces of the infinite OAM basis has remained a challenge. Here, we formalize how the spatial distribution of the pump beam and the nonlinear profile of the crystal can be simultaneously utilized to generate MESs without additional spatial filtering of OAM modes within a subspace. We illustrate our approach with maximally entangled qutrits (d=3)(d=3)(d=3) and ququints (d=5)(d=5)(d=5).