The central achievement of the work is reconfigurability. Non-Abelian braiding, in which the outcome of swapping two objects depends on the order in which the swaps are performed, has previously been demonstrated in superconducting processors, trapped-ion systems, photonic chips and acoustic metamaterials. Those platforms are powerful but require cryogenic temperatures, intricate nanofabrication, or fixed on-chip geometries. The new experiment brings the same mathematical structure into an ordinary liquid crystal cell sitting at ambient conditions, where the relevant objects are micron-scale defect lines entangled around colloidal particles, and where the control knob is simply light.

Disclination lines are the skeletons of disorder within an ordered medium. In a nematic liquid crystal, rod-like molecules align with a local direction called the director; a disclination line marks a seam where that alignment field cannot be smoothly defined, much like the seam on a tennis ball marks a place where the covering cannot lie flat. When colloidal particles are dispersed in the nematic, their surfaces impose orientation constraints on the surrounding director, and defect lines become entangled among the particles, forming stable, topologically protected structures. The team exploited this entanglement by photonically manipulating the colloids, using patterned light to reorient the director field at the cell surface and drive the particles through cooperative molecular reorientations.

By sweeping this optical control, the researchers wove disclination lines into chiral double-helix entanglements, structures in which pairs of defect lines wind around one another in either a left-handed or right-handed twist. The handedness of the helix is not merely decorative; it serves as a binary degree of freedom that the team calls a nematic bit, or nbit. Depending on whether the surface director is rotated counterclockwise or clockwise by the incident light, the entanglement settles into one or the other chiral state, effectively writing a bit into the topology of the defect network. Supplementary videos accompanying the paper show the process unfolding in real time, with double-helix entanglements forming around assemblies of up to nine colloids and even coexisting regions of opposite chirality within a single four-particle structure.

With this encoding in hand, the team implemented a complete set of braid operations, the elementary moves in which defect lines pass over and under one another, and demonstrated their non-commutativity in networks of three lines. In an Abelian world, performing operation A and then operation B yields the same final configuration as performing B and then A. In the nematic platform, the order matters: two braid sequences that differ only in their ordering leave the network in topologically distinct states. This order-dependence is the defining signature of non-Abelian behaviour and the property that makes braided anyons attractive as a basis for fault-tolerant information processing, because the encoded state depends on the global history of exchanges rather than on any local measurement.

A crucial advantage of the soft-matter setting is that the braid gates themselves can be moved. The colloidal particles act as physical gates that pin and route the disclination lines, and by repositioning these particles with optical tweezers and light-driven transport, the researchers reprogrammed the braiding sequence in situ without rebuilding the sample. Small variations in colloid position or local line curvature leave the topological state unchanged, a robustness the team verified directly by perturbing the networks and observing that the encoded configuration survived. The method also extends beyond three-line demonstrations to multiline architectures, suggesting a path toward larger braiding networks assembled from the same elementary components.

Perhaps the most forward-looking contribution is the establishment of an inverse-design framework. Rather than working forward from operations to outcomes, the team developed an algebraic procedure that runs in reverse: given a desired topological transformation, the framework compiles it into prescribed spatial routing of the defect lines together with layer-by-layer phase corrections. This compiler-like capability mirrors how electronic design automation tools translate logic descriptions into circuit layouts, and it transforms the platform from a demonstration apparatus into a programmable one. The researchers note that the scalability of light-driven manipulation makes this design loop practical, since the same optical interface that writes a single bit can in principle address many.

The significance of the result lies in its bridging role. Topological information processing has been dominated by quantum proposals, where non-Abelian anyons would protect quantum states against local noise. Realizing the same braiding algebra in a classical, room-temperature material does not produce a quantum computer, but it provides a tangible, inexpensive laboratory in which non-Abelian logic can be studied, visualized and engineered. The authors position the system as a programmable classical platform for robust topological transformations, one that connects the soft-matter physics of liquid crystals with the emerging field of topological information processing. Because liquid crystals are already the workhorse of display technology, there is also a plausible engineering pathway: the optical and electro-optical toolkits for addressing nematic cells at high resolution are mature and commercially available.

The work also builds on a rich lineage. Knot-theoretic descriptions of nematic defects date back more than a decade, when theorists showed that disclination networks carry invariants analogous to braids and that rewiring operations among them can be classified. Experimentalists later demonstrated reconfigurable knots and links in chiral nematic colloids, and recent theoretical work proposed nematic bits and universal logic gates based on defect topology. What the new study adds is dynamics and control: the ability to actively drive the system through braid operations on demand, to verify non-commutativity experimentally, and to reprogram the network at will. Earlier light-driven studies from the same group had shown collective transport and reconfigurable assembly of nematic colloids and active transformations of disclination networks, providing the technical foundation for the present braiding results.

Looking ahead, the researchers suggest that the platform could serve as a testing ground for algorithms and error models relevant to topological computing, while also raising its own questions about how complex braid networks relax, hold information and fail. The combination of a mathematical structure once confined to abstract group theory with something as tangible as soap-like molecules and glass beads, manipulated by nothing more exotic than patterned light, is a reminder that some of the deepest ideas in physics can be made to run, quite literally, at room temperature. For now, the nematic bits weave their helices quietly under a microscope, but they weave them on command, in any order the operator chooses, and undo nothing by accident.

Subject of Research: Light-driven reconfigurable non-Abelian braiding of disclination lines in nematic liquid crystals

Article Title: Reconfigurable non-Abelian braiding of nematic bits

Article References: Lei, Z., Zheng, X., Zhang, J., Tang, W., Tian, K., Song, G., Asilehan, Z., Chen, Z., Vergara, F., Guan, Y., Zhang, R., Jiang, J., & Peng, C. (2026). Reconfigurable non-Abelian braiding of nematic bits. Nature Materials. https://doi.org/10.1038/s41563-026-02728-x

Image Credits: AI Generated

DOI: 10.1038/s41563-026-02728-x

Keywords: non-Abelian braiding, nematic liquid crystals, topological defects, disclination lines, nematic bits, colloids, topological information processing, soft matter, inverse design, liquid crystal colloids, chiral double helix, optical control

The concept at the heart of the experiment is Floquet engineering, named after the nineteenth-century French mathematician Gaston Floquet, whose theory describes systems subjected to periodic driving. In a Floquet system, the energy bands of a material are no longer the static bands familiar from textbook solid-state physics. Instead, the periodic drive creates replicas of the original bands, called sidebands, separated by multiples of the photon energy. When these replicas hybridize with one another, the effective band structure that electrons experience can be fundamentally transformed. A trivial material can, in principle, acquire the hallmarks of a topological insulator: protected conducting edge channels and a bulk that remains insulating.

Graphene has served as the canonical theoretical playground for this idea ever since theorists predicted that circularly polarized light could gap out its Dirac cones and endow the otherwise gapless material with a topological character. In graphene, electrons behave as massless Dirac fermions moving through two inequivalent valleys in momentum space. Circularly polarized light breaks time-reversal symmetry and imprints opposite topological masses on the two valleys, producing a Chern-like Floquet band structure. The prediction was elegant, but verifying and controlling it experimentally proved extraordinarily difficult, because the light-induced gaps exist only while the driving field is present and they are easily masked by heating, disorder, and the many-body complexity of real solids.

The new experiment overcomes these obstacles by combining an intense mid-infrared driving field with ultrafast time- and angle-resolved photoemission spectroscopy, known as tr-ARPES. In this technique, a pump pulse dresses the graphene electrons with photons while a delayed probe pulse ejects them, allowing researchers to reconstruct the occupied and unoccupied electronic structure with femtosecond temporal resolution. By tuning the polarization, intensity, and timing of the pump pulse, the team could watch the Floquet sidebands emerge, measure the light-induced gaps at the Dirac point, and, most importantly, steer the electron populations within the engineered bands in real time.

The decisive advance is the demonstration of control rather than passive observation. By adjusting the parameters of the optical drive, the researchers could modify the size of the Floquet gaps and redistribute electrons among the light-dressed states, effectively programming the electronic landscape of graphene on demand. The measurements reveal that the dressed electrons follow the instantaneous symmetry of the driving field, so that switching the handedness of the circular polarization reverses the topological character imprinted on the two valleys. This level of command over a transient quantum phase had remained elusive in earlier studies, which succeeded in detecting Floquet states but could not reliably manipulate them.

Timing proved to be as important as intensity. The team found that the Floquet bands form and dissolve on femtosecond timescales, and that a window exists during which the light-induced gaps are well defined before carrier relaxation and phonon scattering wash them out. By probing within this window, the researchers obtained clean spectroscopic signatures of the topological band structure: gaps opening at the Dirac crossings, sidebands displaced by integer multiples of the pump photon energy, and spectral weights consistent with theoretical Floquet calculations. The agreement between the measured spectra and simulations based on the Floquet formalism provides strong evidence that the observed states are genuine light-dressed bands rather than artifacts of the measurement.

The implications extend well beyond graphene. Floquet topological insulators are a testbed for a broader vision in which materials properties are not fixed at synthesis but become dynamically programmable. A topological insulator is prized for its robust, dissipation-resistant edge transport, which makes it a candidate platform for low-power electronics and topological quantum information processing. If such phases can be switched on and off with light, devices could in principle route currents along reconfigurable edge channels at terahertz rates, far faster than conventional transistor switching, and without the need to chemically alter or permanently structure the material. The present work demonstrates the elementary operations, gap control and population steering, that such a scheme would require.

The achievement also sharpens a long-standing debate in the Floquet community about how driven quantum systems reach equilibrium, or whether they avoid it altogether. In principle, continuous driving should continuously pump energy into the electrons and heat the system until the band structure loses meaning. Yet the experiments show that on the ultrafast timescales probed here, a coherent, well-defined Floquet band structure exists long enough to be useful. Understanding the interplay between coherent driving, electron-electron scattering, and phonon-mediated relaxation in this regime is a central question for the field, and the new data provide quantitative benchmarks for theories of nonequilibrium many-body dynamics in driven solids.

Challenges remain before optical control of topological electrons can leave the laboratory. The light-induced phase persists only while the drive is on, so practical devices would need continuous or high-repetition-rate illumination, raising questions about efficiency and heat management. The drive intensities required are substantial, although the use of mid-infrared photons resonant with the material’s interband transitions helps maximize the gap size for a given fluence. Extending the approach to other two-dimensional materials, including topological semimetals and engineered moiré superlattices, could lower the required power and broaden the accessible phases, from Chern insulators to Floquet Weyl semimetals and anomalous Floquet phases with no static counterpart.

Even with those caveats, the study marks a conceptual turning point. For two decades, topological materials have been discovered, characterized, and catalogued as static objects. This work shows that the topology itself can be an operating parameter, adjusted with the twist of a polarization dial and read out within a single optical cycle. The electrons in a Floquet topological insulator are no longer merely passengers on a light-induced band structure; they can now be directed through it. As ultrafast light sources and probe techniques continue to advance, the prospect of circuits whose conducting pathways are written, erased, and rewritten by beams of light moves from theoretical speculation toward experimental engineering.

Subject of Research: Optical control of electrons in a Floquet topological insulator created in light-dressed graphene.

Article Title: Optical control of electrons in a Floquet topological insulator

Article References: Lesko, D. M. B., Weitz, T., Wittigschlager, S., Li, W., Heide, C., Neufeld, O., & Hommelhoff, P. (2026). Optical control of electrons in a Floquet topological insulator. Nature Physics. https://doi.org/10.1038/s41567-026-03429-7

Image Credits: AI Generated

DOI: 10.1038/s41567-026-03429-7

Keywords: Floquet topological insulator, graphene, optical control, topological phases, ultrafast laser, Floquet engineering, light-matter interaction, edge states, condensed matter physics, photoinduced band gaps, Optical, control