The apparently simple problem of the dynamics of electrons confined to a plane with a strong perpendicular magnetic field gives rise to one of the most fascinating phenomena in condensed matter, the fractional quantum Hall effect. This strongly correlated system presents rich physics and has exotic excitations, called anyons, that do not behave like standard particles upon exchange.
Besides being interesting for fundamental physics, anyons might also become useful in the future for more robust forms of quantum computing. At low energies, fractional quantum Hall states are elegantly described by a gauge theory similar to those appearing in high energy physics: the Chern- Simons theory.
In our work, we made significant progress towards engineering anyons in highly controllable quantum systems made of ultracold atoms by realizing for the first time a one-dimensional reduction of the Chern-Simons theory, the chiral BF gauge theory, in a Bose-Einstein condensate.
The experiment used ultracold potassium-39 atoms in two internal states with very different atomic interactions. By coupling these states using light, we linked the interactions of the atoms to their momentum. This led to a chiral system where the atoms interacted differently for positive or negative momenta, and that corresponded to the chiral BF gauge theory. Chiral interactions were demonstrated through the creation of chiral bright solitons: wavepackets which propagate without dispersion when travelling in one direction, but expand as a normal gas when they move in the opposite direction. These solitons had been predicted almost 25 years ago, but had not been realized before. Finally, we observed that the system self-generated an electric force, making the potassium atoms behave as charged particles despite being in reality neutral.
Our result demonstrates that engineering gauge theories with ultracold atoms is under reach, and paves the way towards implementing other models in higher dimensions.