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Journal of Optics

Mathieu–Gauss photons: non-diffraction and self-healing at the quantum regime

Daniel Salamanca-Roldán, Oscar Alejandro Ramírez-Espinosa, Roberto Ramírez-Alarcón, Edgar Medina-Segura, Pablo Yepiz-Graciano, Carmelo Rosales‐Guzmán

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Abstract Quantum entanglement represents one of the most fascinating aspects of quantum mechanics and underpins the advancement of next-generation quantum-based technologies. Of particular interest is quantum entanglement in the spatial degree of freedom of light. As such, in this paper, we analyze a two-photon orbital angular momentum entangled state, decomposed in terms of helical Mathieu–Gauss ( HMG ) modes and generated through a type II spontaneous parametric down conversion process. Furthermore, a spatially-resolved heralded single photon detection system allowed the observation of the transverse spatial distribution of correlated HMG photons and the corroboration of their self-healing and non-diffractive properties. More precisely, we were able to corroborate that HMG photons maintain the same non-diffractive properties of classical HMG beams and that their time-averaged transverse field distribution reconstructs itself upon propagation in the presence of an opaque obstacle.

DOI
10.1088/2040-8986/ae36c0

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Abstract Quantum entanglement represents one of the most fascinating aspects of quantum mechanics and underpins the advancement of next-generation quantum-based technologies. Of particular interest is quantum entanglement in the spatial degree of freedom of light. As such, in this paper, we analyze a two-photon orbital angular momentum entangled state, decomposed in terms of helical Mathieu–Gauss ( HMG ) modes and generated through a type II spontaneous parametric down conversion process. Furthermore, a spatially-resolved heralded single photon detection system allowed the observation of the transverse spatial distribution of correlated HMG photons and the corroboration of their self-healing and non-diffractive properties. More precisely, we were able to corroborate that HMG photons maintain the same non-diffractive properties of classical HMG beams and that their time-averaged transverse field distribution reconstructs itself upon propagation in the presence of an opaque obstacle.
In this work, we provide a complete theoretical and experimental study of a two-photon quantum state entangled in the orbital angular momentum (OAM) degree of freedom of the helical Mathieu-Gauss (HMG) modes. The state is generated by a type II spontaneous parametric down conversion (SPDC) process. Our analysis shows that the generated state is composed by the superposition of two symmetric Bell states with tunable contributions determined by the eccentricity parameter of the HMG modes. The predicted entangled state is confirmed experimentally by measuring the HMG modal joint probability of the SPDC two-photon state and the violation of Bell-type inequalities.
One of the most captivating properties of diffraction-free optical fields is their ability to reconstruct upon propagation in the presence of an obstacle, both classically and in the quantum regime. Here we demonstrate that the local entanglement, or nonseparability, between the spatial and polarization degrees of freedom also experience self-healing. We measured and quantified the degree of nonseparability between the two degrees of freedom when propagating behind various obstructions, which were generated digitally. Experimental results show that even though the degree of nonseparability reduces after the obstruction, it recovers to its maximum value within the classical self-healing distance. To confirm our findings, we performed a Clauser-Horne-Shimony-Holt Bell-like inequality measurement, proving the self-reconstruction of nonseparability. These results indicate that local entanglement between internal degrees of freedom of a photon, can be recovered by suitable choice of the enveloping wave function.
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.
Twisted light, or light with orbital angular momentum (OAM), plays an emerging role in both classical and quantum science, with important applications in areas as diverse as biophotonics, micromachines, spintronics, or quantum information. It offers fascinating opportunities for exploring new fundamental ideas in physics, as well as for being used as a tool for practical applications. One important point is to determine how to generate single photons, and two-photon states, with an appropriate OAM content. Here we describe the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric down-conversion (SPDC) in different non-collinear geometries. These geometries introduce a variety of new features. In particular, we find the OAM of entangled pairs generated in purely transverse-emitting configurations, where the entangled photons counter-propagate perpendicularly to the direction of propagation of the pump beam. The spatial walk-off of all interacting waves in the parametric process also determines the OAM content of the down-converted photons, and here its influence is also revealed.
Orbital angular momentum (OAM) of single photons represents a new optical degree of freedom for the entanglement of photons [1,2]. One physical realization of OAM carrying light beams are the so called Laguerre-Gaussian modes of light with the required helical phase structure. One big advantage over the well known polarization degree of freedom is the possibility of realizing entanglement between two photons with very high quantum numbers. However, the creation of photonic OAM entanglement using the widely used spontaneous parametric downconversion process is limited by the strongly reduced efficiency for higher momenta [3]. We have realized a novel method to create entanglement between two photons with a very high difference in their OAM quantum number and momentum respectively. Furthermore we have explored hybrid entanglement of photons in the OAM and polarization degree of freedom.
Orbital angular momentum (OAM)-entangled states produced by spontaneous parametric down-conversion (SPDC) are considered ideal for realizing high-dimensional entangled states, which have several advantages for quantum technologies. However, the limited sensitivity of current two-photon OAM detectors is a major roadblock not only for realizing such technologies but also for resolving foundational questions, such as OAM conservation in SPDC. The current theoretical understanding is that OAM is not conserved in Type-II SPDC but is conserved in Type-I. Experimentally, although non-conservation in TypeII has not been demonstrated, conservation in Type-I has been reported frequently and has become an underlying assumption for techniques generating high-dimensional OAM entangled states. In this work, we experimentally demonstrate a high-sensitivity two-photon OAM detector, using which, contrary to the current understanding, we report non-conservation of OAM in Type-I SPDC. We attribute this to a spatial walk-off effect and prove it using a framework free of standard phase-matching approximations.