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arXiv:2607.16520

Bridging Relativistic Twisted Fermion Beams and Photonic OAM Flux in Gauged Hopf Lattices: Emergent Topological Analogs

Aaron Michael Kinder

physics.opticsquant-phSubmitted Jul 17, 2026• Announced Jul 21, 2026

Abstract

Recent work has demonstrated non-diffractive topological spin textures (Skyrmion- and meron-like) that persist in the core of diffracting relativistic twisted fermion beams [1]. Here we present numerical simulations of an analogous photonic system: Laguerre-Gaussian (LG) twisted photon packets coupled to a gauged Hopf lattice with discrete flux flywheels. Our results reveal emergent behavior of the same qualitative class, including persistent core features under propagation, mean survival approx 0.150 at critical lambdat = 2 clustering tightly with the mystery scale e^{-2} approx 0.1353 and residual R approx 0.1375, golden-angle correlations in the OAM mode ladder, and topological residuals with long-lived structure. Multi-l simulations further exhibit z-resolved flux transfer and twist dynamics that play a role analogous to probability-current continuity in the fermionic setting. These findings suggest photonic platforms as accessible analogs for exploring topological textures in structured waves, and they formalize a concrete computational bridge between relativistic twisted matter waves and topological photonics.

Comments: Code frozen at: https://github.com/kinaar8340/oam_flux/releases/tag/v0.5-preprint (commit a86062d) Includes full anc/ directory with frozen code, data, and figure scripts. Live demo: https://huggingface.co/spaces/kinaar111/oam_flux

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Recent experiments in moiré quantum materials exhibit quantized Hall states without an external magnetic field, motivating continuum mechanisms based on smooth moiré-periodic pseudospin textures. We present a controlled theory of skyrmion Chern bands generated by such textures. An exact local

SU(2)

transformation reveals an emergent non-Abelian gauge field; for large branch splitting we perform an operator-level Schrieffer-Wolff expansion, yielding a single-branch Hamiltonian together with systematically dressed physical operators that define the projected interacting theory beyond strict adiabaticity. The leading dynamics is governed by a

U(1)

Berry connection whose flux is set by the skyrmion density, while controlled non-adiabatic corrections are fixed by the texture's real-space quantum geometric tensor. In a Landau-level representation built from the averaged emergent field, moiré-periodic modulations induce Umklapp-resolved deformations of Girvin-MacDonald-Platzman kinematics and microscopic sources of excess optical quantum weight above the topological lower bound. Assuming a gapped Hall phase, we further derive a skyrmion-crystal effective field theory with a universal Berry-phase term and a noncommutative magnetophonon. Our results provide experimentally accessible signatures for twisted transition-metal dichalcogenide homobilayers and rhombohedral graphene aligned with hexagonal boron nitride.

Quantum simulation with controllable many-body platforms offers a powerful route to exploring complex phases and dynamics that are difficult to access in natural materials. Among these, topological spin textures such as skyrmions are central to modern condensed-matter physics and play a key role in chiral quantum many-body systems. Their controlled realisation in large, programmable quantum platforms, however, remains an outstanding challenge. Here, we report deterministic generation and site-resolved reconstruction of topological spin textures in a two-dimensional crystal of more than 150 trapped ions. Using globally applied spin-dependent forces, we generate skyrmion configurations and reconstruct the full vector spin field with single-ion resolution, obtaining a winding number of 0.99$\pm

0.02 and a mean local fidelity of 0.87

\pm$0.04. In addition, we implement single-ion-resolved control to deterministically prepare domain-wall states, extending our approach to a broader class of non-uniform spin textures. These results establish trapped-ion crystals as a platform for engineering complex spin textures and open the door to exploring topology-dependent nonequilibrium dynamics in long-range interacting quantum systems.

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.