In principle, one shouldn’t compare apples to oranges. However, in topology, which is a branch of mathematics, one has to do just that. Apples and oranges, it turns out, are said to be topologically the same since they both lack a hole – in contrast to doughnuts or coffee cups, for instance, which both have one (the handle in the case of the cup) and, hence, are topologically equal. In a more abstract way, quantum systems in physics can also have a specific apple or doughnut topology, which manifests itself in the energy states and motion of particles. Researchers are very interested in such systems as their topology makes them robust against disorder and other disturbing influences, which are always present in natural physical systems.
Things get particularly interesting if, in addition, the particles in such a system interact, meaning that they attract or repel each other, like electrons in solids. Studying topology and interactions together in solids, however, is extremely difficult. A team of researchers at ETH led by Tilman Esslinger have now managed to detect topological effects in an artificial solid, in which the interactions can be switched on or off using magnetic fields. Their results, which have just been published in the scientific journal Science, could be used in quantum technologies in the future.
Transport by topology
Zijie Zhu, a PhD student in Esslinger’s lab and first author of the study, and his colleagues constructed the artificial solid using extremely cold atoms (fermionic potassium atoms), which were trapped in spatially periodic lattices using laser beams. Additional laser beams caused the energy levels of adjacent lattice sites to move up and down periodically, out-of-sync with respect to each other. After some time, the researchers measured the positions of the atoms in the lattice, initially without interactions between the atoms. In this experiment they observed that the doughnut topology of the energy states caused the particles to be transported by one lattice site, always in the same direction, at each repetition of the cycle.
“This can be imagined as the action of a screw”, says Konrad Viebahn, Senior Postdoc in Esslinger’s team. The screwing motion is a clockwise rotation around its axis, but the screw itself moves in the forward direction as a result. With each revolution the screw advances a certain distance, which is independent of the speed at which one turns the screw. Such a behaviour, also known as topological pumping, is typical of certain topological systems.
