As a rule, it is not recommended to compare apples with oranges. However, this comparison needs to be made in the field of topology, which is a branch of mathematics. It turns out that apples and oranges are topologically the same because neither of them have a hole – unlike donuts or coffee cups, for example, they have one (a stem in the case of the cup) and are therefore topologically equal.

More abstractly speaking, quantum systems in physics can also have a certain apple or donut topology that manifests itself in energy states and particle motion. Researchers are very interested in such systems because their topology makes them resistant to disorder and other destructive effects that are always present in natural physical systems.

In addition, things become particularly interesting if the particles in such a system interact, that is, if they attract or repel each other, like electrons in solids. However, studying topology and interactions in solids is extremely difficult. A group of researchers from ETH, led by Tilman Esslinger, has succeeded in detecting topological effects in an artificial solid where interactions can be turned on and off by magnetic fields. Their results were recently published in a scientific journal ScienceIt can be used in quantum technologies in the future.

Transport by topology

Zijie Zhu, a graduate student in Esslinger’s lab and first author of the study, and colleagues constructed an artificial solid using ultracold atoms (potassium fermionic atoms) trapped in spatially periodic lattices by laser beams. Additional laser beams caused the energy levels of neighboring lattice nodes to move up and down periodically out of sync with each other. After some time, researchers measured the positions of the atoms in the lattice, initially without interaction between the atoms. In this experiment, they observed that the donut topology of energy states resulted in particles always being transported in the same direction by a single node of the lattice in each repetition of the cycle.

“You can think of it as the movement of a screw,” says Konrad Wieban, a senior postdoctoral researcher on Esslinger’s team. The screwing movement is a clockwise rotation around its own axis, but as a result the screw itself moves forward. In each revolution, the screw advances a certain distance, which does not depend on the rotation speed. This behavior, also known as topological pumping, is typical for certain topological systems.

But what if the screw hits an obstacle? In the ETH researchers’ experiment, it turned out that such an obstacle was created by an additional laser beam that limited the freedom of longitudinal movement of atoms. After about 100 turns of the screw, the atoms appear to hit the wall. In the analogy used above, the wall represents the topology of an apple, where topological pumping cannot occur.

amazing comeback

Surprisingly, the atoms not only stopped at the wall, but suddenly turned back. Thus, although the screw constantly rotated clockwise, it moved backwards. Esslinger and his team attribute this rotation to the two donut topologies in the lattice; One donut rotates clockwise and the other rotates counterclockwise. In the wall, atoms can change their direction of motion by moving from one topology to another.

Now researchers have turned on the repulsive interaction between atoms and watched what happens. And they were faced with a surprise again: Now the atoms were spinning towards the invisible barrier, they could not even reach the laser wall. “Using model calculations, we were able to show that the invisible barrier is created by the atoms themselves due to mutual repulsion,” explains PhD student Anne-Sophie Walter.

Qubit highway for quantum computers

“With these observations, we have taken a major step towards a better understanding of interacting topological systems,” says Esslinger, who studies such effects under an advanced grant from the Swiss National Science Foundation (SNF). As a next step, he wants to conduct further experiments to investigate whether the topological screw is as robust against disorder as expected and how the atoms behave in two or three spatial dimensions.

Esslinger also has some practical applications in mind. For example, the transport of atoms or ions via topological pumping can be used as a qubit highway to deliver qubits (quantum bits) in quantum computers to desired positions without heating them or disrupting their quantum states.