While in three dimensions particles can be classified into bosons and fermions, according to their statistical properties, this classification breaks down in two dimensions and particles with fractional statistics may exist. These exotic objects are called anyons. Among the systems where anyons naturally appear, fractional quantum Hall (FQH) systems are perhaps the most famous. Although the anyonic statistics of the quasihole excitations of these systems has been predicted more than 30 years ago, no clear-cut experimental evidence is available. In this context, I will first review the reasons why particle statistics can be different in three and two spatial dimensions. Then, I will present our proposal for the experimental detection of the quasihole anyonic statistics in an ultracold atomic setup, which, with respect to the previous ones, has the great advantage of only requiring static measurements on the FQH cloud [1]. In conclusions, I will briefly mention the extension of this idea to the case of non-Abelian anyons and to the lattice analogs of the FQH states.

[1] R. O. Umucalilar, E. Macaluso, T. Comparin, and I. Carusotto, Phys. Rev. Lett. 120, 230403 (2018).