January 11, 2021

Dancing Molecules and Two-dimensional Particles

Researchers find a new way of realizing anyons using rotating molecules.

Researchers find a new way of realizing anyons using rotating molecules.


Realization of anyons on the sphere using linear molecules. The red and the blue molecule each rotate around their own vertical axis in opposite directions. Their alignment corresponds to the red and blue points on the sphere respectively, representing the imagined anyons. From figure I to II the molecules make half a rotation, exchanging the positions of the anyons on the sphere. From figure II to III the second half of the rotation occurs and the anyons are back at their original positions. The curved lines underneath them represent the encoded history of the exchange with the red line in the front and the blue line the back forming a so-called braid. © Enderalp Yakaboylu, IST Austria.

Anyons are an elusive kind of quasiparticles, not yet unambiguously observed in experiments. Scientists at the Institute of Science and Technology Austria (IST Austria) in cooperation with Uppsala University now have found a new way of constructing a system of rotating molecules whose behavior corresponds to anyons living on the surface of a sphere. This could offer a promising way of finally observing these intangible quasiparticles and may help in the realization of future quantum computers.

In the counterintuitive realm of quantum mechanics, scientists find strange relations between our three-dimensional world and an imagined two-dimensional world of quasiparticles, which are called anyons. Lead by physicist Enderalp Yakaboylu, researchers from the Lemeshko group and Seiringer group (Morris Brooks) at the Institute of Science and Technology Austria (IST Austria) in collaboration with Douglas Lundholm from Uppsala University have now found a new way of experimentally realizing these so far intangible anyons, possibly aiding efforts to constructing a new kind of quantum computer.

Particle Families

Our everyday world is composed of two families of particles: fermions and bosons. Fermions are for example protons, neutrons, and electrons in the atoms that form matter. Particles of light, so-called photons, on the other hand are bosons. Each of these families of particles follows different physical laws that govern their interactions with each other. One important rule determines what happens when two particles of the same kind exchange places in a given system and how this affects the whole system. For both families it holds that if you exchange two particles twice there is no overall change. For comparison, imagine having two footballs. Switching their places twice brings you back to the original state.

When a great number of individual particles, either fermions or bosons, interact with each other, the governing equations are much too complicated to solve straightforwardly. Instead, scientist constructed a way to describe the collective effect of these interactions in a simplified manner and found that these results behave like a new kind of particle, a so-called quasiparticle. A quasiparticle is not a particle like an electron or photon, but a concept to describe an emerging collective behavior of a complex system.

Living in Two Dimensions

Anyons are such quasiparticles living in an imagined two-dimensional world. This means that there are real physical systems in our three-dimensional world that under the right circumstances behave collectively like these anyons in a two-dimensional world. The exciting thing about anyons is that exchanging the position of two of them twice does not lead to the original configuration of the system, but encodes the history of that exchange. However, finding the right system to construct and observe anyons is very hard and has not been achieved so far in a definitive manner.

For some time now, scientists have proposed to use this effect of encoding the history of exchanging anyons as a very stable carrier of information to use in so-called topological quantum computers. Quantum computers promise marvelous computational power for solving hard problems, but building them has proved to be very difficult because the necessary quantum effects deteriorate very easily. Using anyons and their special feature of encoding their history of exchanging particles may be a solution.

Dancing Molecules

The team around Enderalp Yakaboylu has now devised a new theoretical way of constructing such anyons from an already well-researched physical system. It consists of two linear molecules of two atoms each—one could imagine a straight rod with one atom at each end—that are suspended in a tiny droplet of extremely cold helium at almost absolute zero temperature. When exposing these molecules to a magnetic field they start to rotate and affect each other.

What the scientists found is that the rotation and interactions of these molecules correspond to anyons—the quasiparticles—moving on the surface of an imagined sphere. The exchange of positions of anyons on the sphere then corresponds not to the physical exchange of the two molecules, which would be hard to do in an experiment, but to the interaction of their rotations. This makes it much easier to realize this in an experiment. The constraints given by laws governing the anyons then establish rules for how the molecules can align with respect to each other during their rotation, which in turn could be observed in an experiment.

This new system of realizing anyons may be a first step towards use in topological quantum computers that promise great advances in computational power. Whether this dance of molecules can be realized and whether it will show us the so far elusive anyons will have to be determined by future experiments.

Publication

Morris Brooks, Mikhail Lemeshko, Douglas Lundholm, and Enderalp Yakaboylu. 2021. Molecular Impurities as a Realization of Anyons on the Two-Sphere. Physical Review Letters. DOI: 10.1103/PhysRevLett.126.015301

Funding information

The IST Austria project was partly supported by funding from the Göran Gustafsson Foundation (grant no. 1804), LMU Munich, and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 801770).



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