Laboratoire de Physique Théorique
Toulouse - UMR 5152

While fractional quantum Hall effect (FQHE) was realized experimentally thirty years ago in semiconductor heterostructures, strongly interacting chiral topological phases are still at the center of an important research effort, both as they serve as building blocks of more exotic phases such as fractional topological insulators and as a realization outside of semi-conductor physics is still missing. After a review of the recent development of lattice equivalent of quantum Hall systems, so called Chern insulator, I will describe realizations of strongly interacting chiral phases in cold atomic gases. I will first introduce optical flux lattices, which are continuous models that exhibit topological flat bands with a tunable Chern number. Then, I will show that they host fractional states beyond the FQHE when the partially filled band Chern number is higher than 1. I will then report the emergence of the bosonic integer quantum Hall effect for a filled C=2 band. This is a typical example of a symmetry-protected topological phase that cannot be realized in the absence of interaction. In the last part of my talk, I will explore a new way to create a bosonic FQH state starting from a fermionic system using pairing interaction that can be engineered using Feshbach resonances. As the pairing strength is increased, the system undergoes a phase transition from a fermionic symmetry-protected topological phase to a bosonic intrinsic topological phase. This circumvents many of the current obstacles in the realization of FQH states in cold atomic gases.