To appreciate why this matters, it helps to understand what a skyrmion is. Originally conceived by physicist Tony Skyrme to model atomic nuclei, skyrmions are particle-like topological objects in which a field wraps around a sphere an integer number of times. In optics, a photonic skyrmion is built by sculpting the polarization of light so that, across the beam profile, the spin vector sweeps through every possible polarization state on the Poincaré sphere a whole number of times. That integer winding count, the skyrmion number, is a topological invariant: it cannot be changed by smooth deformations. Local distortions, scattering, turbulence and other perturbations may scramble individual polarization values, but the global winding structure resists such assaults, much like a knot in a rope cannot be untied by gentle shaking.

Previous work had already produced quantum skyrmions in two separate settings. Single-photon skyrmions were generated on chip using nanocavity- or metasurface-coupled quantum emitters, while entangled skyrmions, in which a skyrmionic spin-orbit texture is distributed across two spatially separated photons, were created in bulk crystals using spontaneous parametric down-conversion. What remained missing was a way to bridge the two regimes: to generate entangled skyrmions on an integrated chip, to reconfigure them, and to transfer skyrmion topology coherently from a local single-photon state to a non-local, distributed entangled state. The new experiment closes that gap with a complete integrated architecture.

The heart of the platform is a pair of spin-orbit-locked microring resonators fabricated on a silicon-nitride-on-silica chip with a 310-nanometre-thick device layer. Each resonator supports a clockwise whispering gallery mode with an azimuthal quantum number of 414, and its inner and outer sidewalls carry independently designed angular gratings. When a photon circulates in the resonator, the inner grating scatters it out as a spin-up, left-circularly polarized component carrying zero orbital angular momentum, while the outer grating produces a spin-down, right-circularly polarized component carrying an orbital angular momentum charge of two. The superposition of these two components forms a single-photon skyrmion state with a skyrmion number of two, encoded in the non-separable coupling between the photon’s spin and its spatial degree of freedom.

Generating the entangled partner photon relies on spontaneous four-wave mixing in two on-chip spiral waveguides, each 11.5 millimetres long and tailored to a width of 650 nanometres to maximize the correlated photon-pair generation efficiency. A femtosecond pump pulse coherently drives both nonlinear processes, producing a path-entangled photon pair. Thermo-optic Mach-Zehnder interferometer arrays then route photon A into the microring skyrmion generators and photon B into a two-dimensional grating coupler that converts its paths into horizontal and vertical polarizations. The result is a tensor-product state in which a local single-photon skyrmion coexists with momentum-polarization entanglement between the two photons, all prepared and controlled on a single chip smaller than a fingernail.

The topology transfer itself works much like entanglement swapping. The chip-prepared state can be rewritten in the spin-momentum Bell basis of photon A, revealing four Bell-resolved components, each containing an entangled skyrmion shared between photons A and B. Performing a spin-momentum Bell-state measurement on photon A heralds which component has been produced, and applying the appropriate Pauli correction to photon B completes the mapping: the skyrmion topology originally encoded locally on photon A is now distributed non-locally across the orbital angular momentum of photon A and the polarization of photon B. Quantum state tomography on the resulting states yielded fidelities averaging 89 percent, with retrieved entangled skyrmion numbers of approximately 1.98, in excellent agreement with the theoretical value of two.

The most striking result, however, concerns what happens when noise is deliberately injected. The researchers subjected the transferred entangled skyrmion state to controlled, nearly isotropic noise approximating an effective depolarizing channel, using background and incoherent white-light noise of adjustable intensity. As expected, the state fidelity and purity declined steadily. But the skyrmion number remained essentially unchanged even as the purity fell below 0.34, the point at which the concurrence, the standard measure of entanglement, dropped to zero. In that regime, the state still exhibited non-zero quantum discord, indicating that subtler non-classical correlations persist beyond entanglement and continue to support the topological winding structure. Only when the purity approached roughly 0.25, where isotropic noise overwhelms the original state entirely, did the skyrmion number finally collapse to zero.

The team then tested anisotropic noise channels implemented directly on the chip. By manipulating the on-chip phase of photon B, they realized a phase-flip quantum channel, which in the Poincaré-sphere picture contracts the polarization sphere into an ellipsoid elongated along the S-z direction. Despite continuous degradation of the quantum correlations as the noise ratio increased, the topological number of the entangled skyrmion remained intact up to a critical threshold of 0.5, precisely where the quantum discord vanished. A bit-phase-flip channel, realized by swapping the two paths of photon B through the Mach-Zehnder interferometer, produced the same result: topology preserved until the discord disappeared. These findings establish the skyrmion number as a genuine topological witness of non-classical correlations that extends beyond entanglement, a quantity that survives in a mixed-state regime where conventional quantum state transfer protocols would already have failed.

The implications reach toward the practical challenges of building quantum networks. Distributed quantum computing and quantum communication depend on optical interconnects to move quantum states between nodes, yet entanglement links are notoriously fragile, and error correction or entanglement purification demand substantial overhead in resources and control precision. A topological observable that tolerates noise and even the complete loss of entanglement offers a fundamentally different protection strategy, one baked into the structure of the quantum state itself rather than bolted on through active correction. The authors are careful to note that their experiment does not yet demonstrate an operational advantage for quantum state transfer based on the skyrmion number, but it provides an experimentally accessible foundation for exploring whether topological observables can be harnessed in mixed-state quantum information processing.

Equally significant is the platform itself. The precise, scalable control of photon entanglement, together with flexible thermo-optic routing and switching among different on-chip skyrmion generators, positions integrated photonics as an ideal laboratory for complex topological protocols. The same architecture can, in principle, implement arbitrary local unitary transformations, opening the door to more general topological operations beyond the identity transformations used in this demonstration. As researchers worldwide pursue robust quantum interconnects and distributed quantum technologies, this chip-mediated toolbox for creating, transferring and protecting quantum skyrmions suggests that the future of noise-resistant quantum information may be written not in error-correcting codes alone, but in the topological geometry of light itself.

Subject of Research: On-chip generation and topology transfer of entangled photonic quantum skyrmions

Article Title: Chip-mediated manipulation of photonic quantum skyrmions

Article References: Zhao, H., Zhang, Y., Nape, I., Wu, S., Ji, Y., Zhang, C., Shen, Y., Forbes, A., & Feng, L. (2026). Chip-mediated manipulation of photonic quantum skyrmions. Nature Physics. https://doi.org/10.1038/s41567-026-03487-x

Image Credits: AI Generated

DOI: 10.1038/s41567-026-03487-x

Keywords: quantum skyrmions, integrated photonics, silicon nitride, quantum entanglement, topological protection, quantum discord, orbital angular momentum, microring resonator, spontaneous four-wave mixing, quantum state tomography, quantum interconnects, Nature Physics

Square-root topology is a conceptually elegant trick. Instead of designing a topological insulator directly, one starts from a known topological model, such as the celebrated Su–Schrieffer–Heeger (SSH) chain, and inserts additional sites into the lattice. The resulting ‘square-root’ system is described by a Hamiltonian whose square decomposes into a direct sum of the original parent Hamiltonian and a trivial companion. Because of this algebraic relationship, the child system inherits the topology of its parent, yet its band structure becomes richer: eigenvalues appear in symmetric positive and negative pairs, extra gaps open, and new varieties of boundary states emerge. Theoretical work over recent years has shown that square-root procedures can generate higher-order topological insulators with corner-localized modes, fractionalized topological invariants, and even connections to non-Hermitian and Floquet physics.

Existing photonic demonstrations, however, have faced practical limitations. Most square-root topological states realized so far have lived in microwave or low-frequency terahertz structures such as photonic crystals and coupled waveguides. Plasmonic nanoparticle arrays can push the physics into the visible range, but their unit cells are only nanometers across, making them difficult to fabricate, and long-range dipolar couplings distort their band structures away from the ideal tight-binding picture. The new work circumvents both problems by turning to plasmon-polaritonic systems, in which a chain of circular air cavities is embedded in a metallic background. These structures support designer surface modes whose effective couplings depend on lattice spacing in a controlled way, while long-range interactions decay exponentially and can be safely neglected.

The one-dimensional design consists of circular air cavities, each 120 nanometers in radius, arranged in unit cells of four cavities with a lattice constant of 1500 nanometers—dimensions comfortably accessible to modern nanofabrication. The metallic background is modeled with a Drude-like dielectric function tuned to visible-range operation, using parameters characteristic of gold. The four-cavity unit cell can be understood as a composite of a standard dimerized SSH chain and a uniformly spaced cavity chain. Mathematically, the square of the resulting Hamiltonian equals the direct sum of the cavity-chain Hamiltonian and the parent SSH Hamiltonian, which means the square-root system inherits the eigenvalues of the SSH model with an added sign-symmetric partner, and its band gaps track those of the original chain. When the intracell and intercell spacings are equal the gaps close; making them unequal opens two gaps, exactly as in the parent SSH physics.

The topological character follows from the quantized Zak phase, the standard one-dimensional invariant computed from the Berry connection across the Brillouin zone. When the intracell coupling is weaker than the intercell coupling, the Zak phase equals π and edge states appear inside the gap—a hallmark inherited by the square-root descendant. Because the inserted sites are themselves topologically trivial, the child system’s invariants are not strictly quantized, but the protected boundary physics survives. Simulations of finite chains show edge modes emerging symmetrically about zero energy whenever the dimerization ratio exceeds unity, confirming that the square-root construction transfers the parent’s boundary states intact.

The researchers then extended the idea to two dimensions, building a square-root lattice from a two-dimensional SSH model combined with a uniformly spaced cavity array, giving six cavities per unit cell. Here the inheritance relation becomes particularly striking: the two-dimensional square-root eigenvalues consist of a zero band together with plus-and-minus pairs of the parent model’s eigenvalues, producing a band structure perfectly symmetric about the horizontal axis. Because long-range couplings are negligible in this plasmon-polaritonic platform, the simulated band structures match the ideal theoretical predictions far more cleanly than in nanoparticle systems, where such couplings blur the picture.

Two dimensions also bring higher-order topology into play. In a conventional two-dimensional SSH lattice, inversion and chiral symmetries enforce degenerate edge states, while corner states are often buried within the bulk bands, limiting their usefulness. In the square-root lattice, the inserted sublattice breaks inversion symmetry even though chiral symmetry is preserved. This symmetry reduction lifts the degeneracy of mid-gap states, yielding spectrally isolated, non-degenerate corner modes alongside multiple edge channels. Numerical spectra of finite two-dimensional lattices reveal single corner states sharply localized at the structure’s corners and multiple, doubly degenerate edge states running along its sides—a combination absent from the parent model. Direct excitation simulations, using a point source inside a finite lattice with a dimerization ratio of 1.1, successfully launch both edge and corner modes at distinct visible-range frequencies near 679 terahertz.

Robustness, the defining virtue of topological states, was tested against two kinds of realistic imperfections: random displacement of cavity positions and outright deletion of sites. Position deviations of 30 and 60 nanometers shifted the corner-mode frequencies by only 2.58 and 3.18 gigahertz respectively, while deleting 5 and 15 cavities produced shifts of 6.52 and 4.12 gigahertz. In every case the in-gap edge and corner states persisted, demonstrating that the square-root topology withstands geometric disorder. Material loss, an inevitable feature of plasmonics at visible frequencies, was also included using gold’s attenuation coefficient; the topological modes survived, with the corner mode exhibiting a quality factor of 19.2—modest, but characteristic of plasmonic platforms in this spectral range.

The authors emphasize that the proposed structures are experimentally achievable with current techniques. Feature sizes of 1500-nanometer lattice constants and 120-nanometer cavity radii fall well within the resolution of electron-beam lithography, and electron-beam evaporation of gold produces nanofilms in the 20-to-50-nanometer range with thickness deviations of roughly two nanometers. Fabrication tolerance is further helped by the fact that the topological phase depends only on the dimerization condition, which random position errors do not overturn. Taken together, the results deliver square-root topological edge and corner states at visible frequencies in a platform that is both easier to prepare than nanoparticle arrays and cleaner in its band structure than microwave analogues, expanding the practical toolkit for topological photonics and pointing toward mode-selective, defect-tolerant nanophotonic devices.

Subject of Research: Square-root topological states realized in visible-range plasmon-polaritonic cavity systems

Article Title: Realization of square-root topology in plasmon-polaritonic system

Article References: Fan, Y. (2026). Realization of square-root topology in plasmon-polaritonic system. Results in Optics, 25, Article 101144. https://doi.org/10.1016/j.rio.2026.101144

Image Credits: AI Generated

DOI: 10.1016/j.rio.2026.101144

Keywords: topological photonics, square-root topology, plasmon-polaritons, SSH model, corner states, edge states, Zak phase, higher-order topology, gold nanocavities, visible light, topological protection, nanofabrication