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arXiv:2607.03474

Non-Diffractive Topological Spin Textures of Relativistic Twisted Fermion Beams

Andrei Afanasev, Carl E. Carlson

physics.opticsquant-phSubmitted Jul 3, 2026• Announced Jul 6, 2026
arXivHTMLPDF

Abstract

In optics and acoustics, in structured beams, non-diffracting polarization measures in clearly diffracting beams, and spin direction distributions in the core of these waves that have Skyrmionic behavior have been found. We here study the equivalents of these for fermions and show that in corresponding circumstances the non-diffractive spin textures persist independently of spin, statistics, or kinematics (or propagation speed of the structured wave). As a part of the study, we present LG solutions for Dirac particles valid for both relativistic and non-relativistic kinematics.

Comments
7 pages, 3 figures

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In optics and acoustics, in structured beams, non-diffracting polarization measures in clearly diffracting beams, and spin direction distributions in the core of these waves that have Skyrmionic behavior have been found. We here study the equivalents of these for fermions and show that in corresponding circumstances the non-diffractive spin textures persist independently of spin, statistics, or kinematics (or propagation speed of the structured wave). As a part of the study, we present LG solutions for Dirac particles valid for both relativistic and non-relativistic kinematics.
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We report universal skyrmionic spin textures in the cores of optical and acoustic vortex beams, described within the framework of Laguerre-Gaussian modes. We analytically demonstrate nondiffractive propagating spin merons, independent of whether the field is transverse or longitudinal, with their sign controlled by the wavefront helicity. Experimental confirmation is provided in acoustics through full three-dimensional measurements of the velocity vector field. Although these phenomena are intrinsic to vortex cores, we also show that the claimed universality breaks down for higher-order topological charges, depending on the carrier mode, here exemplified using the Bessel framework.
Space-Time Wave Packets (STWPs) have enabled numerous nontrivial properties, such as tunable group velocities, nondiffraction and nonlocal spin textures in optical fields. However, this has not been properly studied in matter waves. Here, we investigate free-electron STWPs, which are propagation-invariant and group-velocity-tunable matter wave packets, constructed by constraining the spatiotemporal spectrum of the electron wavefunction in momentum space. Due to the unique dispersion of free-electrons, the electron STWP can carry two different topologies, and host both meron and skyrmion topological textures in momentum space. We demonstrate the topological phase transitions and tunable skyrmion numbers by spectral geometry tuning. We also show the topologically robust propagation of the electron pulses and corresponding real-space skyrmionic expectation value textures encoded within each single electron wavefunction. Our results open a platform for topological free-electron wavepackets uses in sensing and information transfer.
The ability of structured light to mimic exotic topological skyrmion textures encountered in high-energy physics, cosmology, magnetic materials, and superfluids has recently received considerable attention. Despite their promise as mechanisms for data encoding and storage, there has been a lack of studies addressing the transfer and storage of the topology of optical skyrmions to matter. Here, we demonstrate a high-fidelity mapping of skyrmion topology from a laser beam onto a gas of cold atoms, where it is detected in its new non-propagating form. Within the spatial overlap of the beam and atom cloud, the skyrmion topological charge is preserved, with a reduction from Q ≃ 0.91 to Q ≃ 0.84, mainly due to the beam width exceeding the sample size. Our work potentially opens novel avenues for topological photonic state storage and the analysis of more complex structured light topologies.
The Dirac equation stands as the cornerstone of relativistic quantum mechanics, successfully predicting spin and antimatter. However, its derivation is typically presented as a formal algebraic requirement—the linearization of the Hamiltonian—without a clear physical ontology explaining why nature demands such a structure. In this work, building upon a previously established model of particles as topologically anchored wave-defects in a continuous medium, we demonstrate that the Dirac equation is not merely an algebraic curiosity but a structural necessity. We show that the requirement to describe the causal, first-order evolution of a relativistic standing wave compels the state variable to possess a multi-component spinor structure. We explicitly derive the Clifford algebra of the dynamical operators and identify the emergent 4-component state space with the physical degrees of freedom of the defect: a local vibrational duality (Spin) coupled to a global topological orientability (Charge). Thus, the ”quantum strangeness” of the fermion—its spin-1/2 nature and antiparticle partner—are demystified, emerging as the natural description of a relativistic object with non-trivial topology.