How solitons bend time, space and rules

If it walks like a particle, and talks like a particle… it probably isn't a particle. A topological soliton is a special kind of wave or dislocation that behaves like a particle: it can move but cannot spread out and disappear as you would expect, for example, from a ripple on the surface of a pond. In a new study published in natureResearchers from the University of Amsterdam have demonstrated the unusual behavior of topological isolations in a robotic metamaterial, something that could be used in the future to control how robots move, sense their surroundings and communicate.

Topological isolates can be found in many places and on many different length scales. For example, they take the form of kinks in Telephone wires are coiled And large molecules such as proteins. On a completely different scale, A Black hole It can be understood as a topological soliton in the fabric of space-time. Solitons play an important role in biological systems, being related to living organisms Protein folding And Morphology – Development of cells or organs.

The unique features of topological solitons—that they can move but always retain their shape and cannot suddenly disappear—are particularly interesting when combined with so-called nonreciprocal interactions. “In such an interaction, factor A interacts with factor B differently from the way factor B interacts with factor A,” explains Jonas Veenstra, a doctoral student at the University of Amsterdam and first author of the new publication.

“Non-reciprocal interactions are common in society and complex living systems, but have long been ignored by most physicists because they can only exist in a system outside of equilibrium,” Veenstra continues. By introducing non-reciprocal interactions into materials, we hope to remove the boundaries between materials and machines and create living or lifelike materials.

The Automated Materials Laboratory where Veenstra conducts his research specializes in design metamaterials: Artificial materials and robotic systems that interact with their environment in a programmable manner. The research team decided to study the interplay between non-reciprocal interactions and topological isolations almost two years ago, when students Anahita Sarvi and Chris Ventura Minnersen decided to pursue their research project for the master's course “Academic Skills for Research”.

The soliton and anti-soliton automata lie on the boundary between the left- and right-leaning parts of the chain. Each blue rod is connected to its neighbors with pink rubber bands, and there is a small motor under each rod that makes interactions between adjacent rods non-reciprocal. Credit: Jonas Veenstra/UvA

Soliton moves like a domino

The soliton host metamaterial developed by the researchers consists of a series of rotating rods linked together by elastic bands – see figure below. Each rod is mounted on a small motor that applies a small force to the rod, depending on how it is oriented relative to its neighbors. Most importantly, the applied force depends on which side the neighbor is on, making the interactions between adjacent bars non-reciprocal. Finally, the magnets on the bars are attracted to magnets placed next to the chain so that each bar has two preferred positions, rotated either to the left or to the right.

The isolates found in this metamaterial are the sites where the left- and right-spinning parts of the chain meet. Complementary boundaries between right- and left-rotated string sections are called antisolitons. This is similar to the kinks in old-fashioned coiled telephone wire, where sections of wire that rotate clockwise and counterclockwise meet.

When the motors in series are turned off, the solitons and counter-solitudes can be manually driven in any direction. However, once the motors – and thus the mutual interactions – are triggered – the solitons and antisolons automatically slide along the chain. They both move in the same direction, at a speed determined by the non-reciprocity property imposed by the motors.

Feenstra: “Much research has focused on moving topological solitons by applying external forces. In the systems studied so far, solitons and anti-solitons have been found to naturally move in opposite directions. However, if you want to control the behavior of (anti-solitons) ), you may want to push them in the same direction. We have discovered that non-reciprocal interactions achieve just this. The non-reciprocal forces are proportional to the spin generated by the soliton, such that each soliton generates its own driving force.

The movement of solitons is like the fall of a series of dominoes, each one toppling the next. However, unlike dominoes, non-reciprocal interactions ensure that the “topple” can only happen in one direction. While a domino can only fall once, a soliton moving along the metamaterial simply sets up the chain for the anti-soliton to move across it in the same direction. In other words, any number of isolates and anti-isolates can move through the chain without needing to be “reset.”

Motion control

Understanding the role of nonreciprocal drive will not only help us better understand the behavior of topological solitons in living systems, but could also lead to technological advances. The mechanism that generates the unidirectional self-driving solitons revealed in this study could be used to control the movement of different types of waves (known as wave steering), or to provide metamaterial with a basic information-processing ability such as filtering.

Future robots could also use topological silos for basic robotic functions such as movement, signaling, and sensing their surroundings. These functions will no longer be controlled from a central point, but will emerge from the sum of the robot's active parts.

Overall, the domino effect of solitons in synthetic materials, now an interesting observation in the laboratory, may soon begin to play a role in various branches of engineering and design.

Reference: “Non-reciprocal topological isolations in active metamaterials” by Jonas Veenstra, Oleksandr Gamayon, Xiaofei Guo, Anahita Sarvi, Chris Ventura Minnersen, and Corentin Collet, 20 March 2024, nature.
doi: 10.1038/s41586-024-07097-6