For the first time, scientists used electric pulses to fuse and split vortex knots created inside chiral nematic liquid crystals (LCs), enabling reversible switching between different knotted forms. The knots, created by scientists at Hiroshima University, the University of Colorado-Boulder, and the University of Illinois at Chicago, remain stable when undergoing the processes of fusion and fission. The fusion and fission of chiral vortex knots could be used to control light and tune light-based applications. Fusion and fission of topological structures like vortex knots are believed to occur deep inside quantum and magnetic materials and to unfold at scales too tiny and fast to observe directly. In contrast, the fusion and fission of the particle-like vortex knots created by the researchers appear at a scale that can be seen and controlled in real time. Vortex knots inside a chiral nematic liquid crystal. Courtesy of the University of Colorado, Boulder/Ivan Smalyukh. By making these topological transformations directly visible and controllable, the team provides a physical testbed for mathematical ideas that until now have lived mostly on paper. The results also point to a potential route toward the development of knot-based electro-optic and photonic technologies. In addition to demonstrating the mathematical knot theory at work, the electric switching of vortex knots could enhance the electro-optic potential of LCs. Toward this end, the team explored how low-voltage electric fields can guide controlled transformations of stable, Kelvin-atom-like vortex knots in chiral LCs through fusion, fission, and more complex relinking of knots. The team created a stable environment for the vortex knots by tuning the helical pitch of the chiral nematic LC molecules between 5-10 μm and confining the liquid between transparent, electrode-coated glass plates. To create the knots, the researchers used holographic laser tweezers that locally melted small regions of the LC. As the regions cooled, the material relaxed into twisted, knotted, 3D, particle-like configurations known as heliknotons. Using indium tin oxide (ITO) electrodes, the researchers applied sub-second voltage pulses to modulate molecular alignment. By raising or lowering the voltage, the researchers found that they could make individual knots expand, shrink, merge, or divide. “We unexpectedly observed that knot fusion is reversible,” researcher Darian Hall said. Fused knots tended to remain together to minimize free energy. However, a rapid reduction in the applied voltage caused the knots to separate again. After extensive testing, the team identified the specific electrical pulse durations and voltage levels required to reliably control fusion and fission. The physical system created by the researchers followed the rules of knot theory. When two knots fused, vortex-line segments with opposite twists canceled out and formed new composite knots, which later split apart when the voltage was reversed. These processes occurred at sub-second timescales, and matched mathematical operations such as band surgeries and connected sums. According to the researchers, the LC demonstrated topological manipulations that were once only described in diagrams. The researchers mapped out how different types of reconnections led to distinct outcomes. In the uniquely stable chiral LC system, some reconnections did not simplify knots, but instead built new, long-lived structures, like composite knots and multi-loop links. To confirm that these changes were topological, the researchers tracked the system’s topological charge and found that it remained constant even as the knots fused or split. The experiments and simulations also uncovered the significant connection between chirality and topology. Reversing the molecular chirality of the LC host from left-handed to right-handed also reversed the handedness and charge of every vortex knot inside the LC. This showed that molecular chirality not only stabilized the knots, but also determined their handedness. LC vortex knots are an example of organized matter whose stability and behavior come from how the material is arranged as well as what it is made of, and could offer new ways to manipulate light. For example, imprinting light with a robust topological structure could enable properties such as orbital angular momentum transfer and information encoding, and new types of light-matter interactions. “The current trillion-dollar-per-year, liquid-crystal-based industries globally are already well equipped to build their next-generation technologies based on switching and fusing knots instead of just smoothly rotating liquid crystal molecules,” professor Ivan Smalyukh said. Smalyukh believes that knotted LCs could open the door to radically new technologies, from unconventional computation, data storage, and advanced displays, to telecommunications, microactuators, and artificial muscles — all enabled by topological control founded on knot theory. The research was published in Nature Physics (www.doi.org/10.1038/s41567-025-03107-0).