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arXiv:2606.28176

Direct Observation of X-ray Double-Slit Interference in Momentum Space

Fugui Yang, Xiaoxiao Liang, Tianchong Zhang, Xiaowei Zhang

Published Jun 26, 2026• 0 citations
arXivHTMLPDF

Abstract

Young's double-slit experiment is conventionally deemed a spatial phenomenon emerging from free-space transport. In this Letter, we invert this perspective to demonstrate that Young's interference can be accessed directly as a pure momentum-space observable. Using a perfect-crystal diffraction to project the field's reciprocal-space profile immediately downstream of the aperture, we resolve the complete hard X-ray double-slit fringe structure without any propagation arm, focusing optics, or imaging detector. This direct capture of the field's invariant momentum marginal establishes a compact, lensless, and propagation-free approach to coherence diagnostics, proving that the fundamental physics of wave interference can be detached from real-space propagation.

DOI
10.48550/arxiv.2606.28176

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Young's double-slit experiment is conventionally deemed a spatial phenomenon emerging from free-space transport. In this Letter, we invert this perspective to demonstrate that Young's interference can be accessed directly as a pure momentum-space observable. Using a perfect-crystal diffraction to project the field's reciprocal-space profile immediately downstream of the aperture, we resolve the complete hard X-ray double-slit fringe structure without any propagation arm, focusing optics, or imaging detector. This direct capture of the field's invariant momentum marginal establishes a compact, lensless, and propagation-free approach to coherence diagnostics, proving that the fundamental physics of wave interference can be detached from real-space propagation.
Young's classic double-slit experiment demonstrates the reality of interference when waves and particles travel simultaneously along two different spatial paths. Here, we propose a double-slit experiment in momentum space, realized in the free-space elastic scattering of vortex electrons. We show that this process proceeds along two paths in momentum space, which are well localized and well separated from each other. For such vortex beams, the (plane-wave) amplitudes along the two paths acquire adjustable phase shifts and produce interference fringes in the final angular distribution. We argue that this experiment can be realized with the present-day technology. We show that it gives experimental access to the Coulomb phase, a quantity which plays an important role in all charged particle scattering but which usual scattering experiments are insensitive to.
This work presents a structural reexamination of Young’s double-slit experiment by identifying a missing stage in its standard formulation and restoring it within a finite, geometry-based framework. The conventional treatment assumes continuous propagation, neutral boundaries, and observation on a single fixed screen, reducing the experiment to a geometric division of a continuous entity. Using exact geometry, interference is described by the condition , which defines a family of hyperbolas in space. From the triangle inequality, the number of interference fringes for monochromatic light is shown to be finite and exactly determined. The commonly observed linear fringe pattern arises from the far-field approximation and represents only a partial cross-section of this global structure. A central result of this work is the identification of the in-slit stage as a necessary part of the experiment. The slit is treated as a finite region in which particles interact with boundary-defined electromagnetic environments, leading to directional redistribution prior to propagation. This interpretation is supported by an asymmetric single-slit experiment using different materials, which produces a reversible asymmetric pattern inconsistent with a purely geometric model. The framework is extended to limiting and classical cases, including tiny apertures and diffraction phenomena such as the Poisson spot, where symmetry and lack of comparison may conceal boundary-dependent effects. The suppression of interference in which-way detection experiments is interpreted as a modification of the electromagnetic environment within the slit. These results show that interference in Young’s experiment is a finite, spatial, and timing phenomenon that cannot be fully described by post-slit geometry alone. Restoring the in-slit interaction provides a complete factual description and introduces material-dependent effects absent from standard treatments.
Modern understanding of light has fluctuated between particle and wave theory. The classic double slit experiment provided seemingly conclusive support for wave theory of light with its resultant fringe patterns thought to only be due to wave interference. However, interference junctures of light have never been directly visualized. We investigated the double slit experiment and its fringe pattern through novel techniques of direct visualization of light propagation in the free space after slit exit in order to validate this interference principle. A cloud chamber and gel media were developed to visualize otherwise invisible light pathways. Coherent light was observed in these environments in settings of diffraction, refraction, and reflection. Experimental generation of distinct, isolated light strands after diffraction through double slits were visualized. Discrete light strands, not waves, were noted as light propagated through free space. Light strands were visualized directly creating the pseudo-interference fringe pattern, counter to the concept of wave interference. Novel visualization of light strands supports the particle theory of light and provides an alternative to wave theory. The finding that diffractive fringe patterns and other observations of light can be explained in some situations by the phenomena of discrete radiating strands, not wave interference, may have implications in physics, quantum mechanics, and technology.
We show, both analytically and experimentally, that under common experimental conditions the interference pattern produced in a classic Young's double-slit experiment is indistinguishable from that generated by means of a doubly refracting uniaxial crystal whose optic axis makes a skew angle with the light propagation direction. The equivalence between diffraction and crystal optics interference experiments, taken for granted by Arago and Fresnel in their pioneering research on the interference of polarized light beams, is thus rigorously proven.
The quantum interference phenomenon was observed in Young’s double-slit experiment using a single photon, and then, the validity of quantum mechanics was demonstrated. However, the reason these fringes appear has not been completely explained yet because photon motion has not been investigated in detail. We found a method to observe the motion of photons using the properties of optical fibers and showed vector diagrams of the photon motion near the double-slit. The photons gradually changed their direction while intersecting and formed interference fringes. In addition, utilizing the mode property of the fiber, we observed fringes at its output end, even when one of the two interfering waves could not transmit through the fiber.