Solitons Drift Predictably across Complex Materials Due to Topological Constraints

Nonlinear Thouless pumping, the controlled flow of energy within materials, now extends beyond repeating, periodic structures to encompass quasiperiodic lattices, which possess a more disordered, fractal-like arrangement. Xiao-Xiao Hu and colleagues at the Lanzhou University and Ningbo University, achieved this by showing how solitons, a type of wave, reconstruct the lattice itself, creating an emergent topological structure governing their movement. Solitons moving through quasiperiodic lattices can reconstruct the material, creating a hidden topological structure that governs their movement.

These lattices, unlike traditional repeating structures, have a more disordered, fractal-like arrangement, allowing for unique wave behaviour. The controlled movement of energy, known as Thouless pumping, has been achieved in quasiperiodic lattices, which exhibit a more disordered, fractal-like arrangement. Xiao-Xiao Hu and colleagues at the Lanzhou University and Ningbo University, relied on the behaviour of gap solitons, a self-reinforcing pulse of light that maintains its shape as it travels, which actively reshape the lattice itself. This reconstruction creates an underlying topological structure that dictates how these solitons move, enabling a remarkably stable flow of energy. This discovery has implications for understanding soliton behaviour in complex materials, but the limits of this control and potential applications require further investigation. Traditionally, Thouless pumping relies on the adiabatic transport of electrons or energy across a band structure, driven by a spatially varying parameter; however, extending this concept to nonlinear systems and, crucially, to quasiperiodic lattices, introduces significant complexities due to the absence of strict translational symmetry.

Gap solitons reshape quasiperiodic lattices enabling enhanced topological control

Nonlinear Thouless pumping has now been achieved in quasiperiodic lattices, resulting in a 25-fold increase in controllable switching between topological pumping, drifting, and localization compared to previous periodic lattice systems. The breakthrough overcomes limitations previously imposed by the need for discrete translational symmetry, a requirement absent in quasiperiodic lattices and therefore presenting a significant challenge. Gap solitons, self-reinforcing pulses of light, actively reshape the lattice, inducing an emergent topological structure that governs their movement and provides a new mechanism for control. The quasiperiodic potential is typically generated using a Fibonacci sequence or similar aperiodic arrangement, creating a lattice with long-range order but lacking the perfect periodicity of conventional structures. This aperiodicity introduces unique challenges for wave propagation, as the standard Bloch theorem no longer applies, and energy bands become fragmented, leading to the formation of localized states.

Soliton reconstruction enables occupation of a single topological band, realising quasi-quantized pumping; perturbations disrupt this band, driving solitons into a controllable drifting regime constrained by a critical rational approximant. Within quasiperiodic lattices, solitons exhibit predictable behaviour, revealing a critical order of rational approximation, denoted as *n c *, which dictates the transition between quantized and non-quantized transport. Analysis of two irrational ratios, √3/3 and √5/5, demonstrated that for approximant orders less than or equal to *n c *, soliton displacement aligns with a specific Chern number, a topological property, resulting in quantized movement; the ratio remained locked near −1 for √3/3 and near 1 for √5/5. Beyond this critical order, displacement deviates, converging towards a non-quantized drift value, yet remains constrained by the topology of the critical approximant Hamiltonian. The Chern number, a topological invariant, characterizes the band structure and quantifies the winding of the wave function in momentum space; its preservation during soliton propagation ensures the robustness of the quantized transport. Coupled optical waveguide array simulations further validated this mechanism, confirming the universality of the observed phenomena; translating this precise control to strong, real-world photonic devices remains a significant engineering challenge. These simulations, based on the paraxial wave equation, accurately model the propagation of light within the quasiperiodic lattice, allowing researchers to verify the theoretical predictions and explore the parameter space. The observed 25-fold increase in control represents a substantial improvement over previous systems, opening up new possibilities for advanced optical functionalities.

Strong soliton transport survives structural disorder in quasiperiodic lattices

Controlling light propagation within materials holds the potential to revolutionise optical computing and sensing. This work demonstrates a new level of control over light pulses, known as solitons, by exploiting their ability to reshape the structures they traverse. While the ‘Thouless pumping’ effect was previously demonstrated in regularly ordered materials, extending it to the more disordered arrangement of quasiperiodic lattices presented a significant hurdle. The ability to manipulate solitons in this manner could lead to the development of novel optical devices with enhanced performance and functionality, such as all-optical switches, routers, and sensors.

Disturbances can easily push the system into a less predictable state, and concerns remain regarding practical application of these findings; however, the underlying structure of the lattice still exerts a powerful influence on light propagation, suggesting durability even with imperfections. This durability prompts investigation into the limits of this control in more complex, three-dimensional systems, and the potential for manipulating light’s behaviour in materials with greater structural complexity. The resilience of the soliton-based pumping mechanism to structural imperfections is particularly noteworthy, as it suggests that the technology could be implemented in real-world materials with inherent defects. Further research is needed to quantify the level of disorder that can be tolerated while maintaining stable soliton transport.

This method of directing energy flow extends from simple repeating structures to the more disordered arrangement of quasiperiodic lattices. Reconstruction generates a hidden topological structure, dictating soliton movement and enabling a stable, predictable flow of energy. The ability to switch between controlled pumping, drifting and complete localisation by adjusting the lattice or nonlinearity now prompts investigation into the limits of this control, particularly regarding the impact of increased dimensionality and material complexity. The interplay between nonlinearity and topology in quasiperiodic lattices is a relatively unexplored area of research, and this work provides a valuable foundation for future investigations. Understanding how these effects scale with dimensionality and material properties will be crucial for realising the full potential of this technology.

Researchers demonstrated a nonlinear topological pumping of gap solitons within quasiperiodic lattices, where local nonlinearities reconstruct the lattice potential itself. This reconstruction creates a topological structure that governs soliton dynamics, allowing for a controlled and predictable flow of energy. While disturbances can disrupt fully quantized pumping, soliton transport remains constrained by the lattice’s underlying topological properties. The authors suggest further work will focus on quantifying the level of disorder tolerable while maintaining stable soliton transport.