How quantum mechanics can make soundproofing

This mechanical model consists of 270 pendulums connected by small springs. The pendulums behave just like a topological insulator. The video below shows them in action. (Credit: Heidi Hostettler/ETH Zurich)

New research suggests the road from abstract theory to practical applications doesn’t need to be very long. A mechanical use of a quantum mechanical phenomenon could soon be used for soundproofing.

For several years now, theoretical physicist Sebastian Huber of ETH Zurich has focused on so-called topological insulators, i.e., materials whose ability to conduct electric current originates in their topology.

The easiest way to understand what “topological” means in this context is to imagine how a doughnut can be turned into a coffee cup by pulling, stretching, and molding—but without cutting it.

mug doughnut topology
Topologically speaking, doughnuts and coffee cups are identical. (Credit: Sebastian Huber/ETH Zurich)

Topologically speaking, therefore, doughnuts and coffee cups are identical, and by applying the same principle to the quantum mechanical wave function of electrons in a solid we obtain the phenomenon of the topological insulator.

This is advanced quantum physics, highly complex and far removed from everyday experience. Nevertheless, Huber and his collaborators have now managed to make these abstract ideas very concrete and even to come up with a possible application in engineering.

270 pendulums

In the beginning, Huber asked a simple question: is it possible to apply the principle of a topological insulator to mechanical systems? Normally, quantum physics and mechanics are two separate worlds.

In the quantum world, particles can “tunnel” through barriers and reinforce or cancel each other as waves, whereas everyday mechanics deals with falling bodies or the structural analysis of bridges.

Huber and his colleagues realized, however, that the mathematical formulas describing the quantum properties of a topological insulator can be rearranged to look exactly like those of a well-known mechanical system—an array of swinging pendulums.

In particular, just like their quantum mechanical counterparts, the mechanical formulas predicted so-called edge states. In such states an electric current (or, in the case of pendulums, a mechanical vibration) flows along the edges of the material, while inside the system nothing happens.

“From a theoretical point of view that was a beautiful result,” says Huber, “but, of course, it is easier to convince people if you also show it in practice.”

As reported in Science, Huber and colleagues built a mechanical model consisting of 270 pendulums that are arranged in a rectangular lattice and connected by small springs. Two of those pendulums can be mechanically excited, meaning that they can be shaken back and forth with a particular frequency and strength. Little by little, the spring couplings cause the other pendulums to start swinging as well.

Eventually, for a particular excitation frequency the physicists saw what they had been hoping for: the pendulums inside the rectangle stood still, whereas those along the edge vibrated rhythmically, causing a “wave” to flow around the rectangle. In other words, the coupled pendulums did, indeed, behave just like a topological insulator.

Jittery robot arms

What started out as a pipe dream and a nice gimmick for Huber could soon become a useful tool. The mechanical edge states of the coupled pendulums, it turns out, are so robust—”topologically protected,” in technical language—that they persist if the array of pendulums is disordered and even if a part of the rectangle is removed.

Such properties would be interesting, for instance, in sound and vibration insulation, which is important in various areas such as industrial production, where robot arms have to place objects precisely and without jittering. Moreover, one can imagine materials that convey sound in one direction only, or others that focus sound like a lens.

“Such applications are very challenging, but still realistic,” says Chiara Daraio, professor for mechanics and materials at ETH Zurich. Of course, the mechanical systems would first have to shrink considerably—Huber’s pendulums are, after all, roughly one foot eight inches long and weigh over a pound.

The engineers are already building a new device that works without pendulums and that will only be a about an inch in size.

Source: ETH Zurich