# C5

## Gauge fields and topological states with cold atoms in optical lattices

### Martin Weitz

Topological states of matter are an active new frontier of research, and provide a novel means for the generation and stabilization of quantum systems, which is the central topic of project area C of this collaborative research center. This project aims at the realization of strong gauge fields and topological states, using ultra-cold erbium atoms in far-detuned optical fields. We plan to reach physics beyond the meanfield level entering the quantum Hall regime, where atoms are effectively strongly interacting.

Within the project we will investigate quantum many-body states with topological order, using erbium atoms in a synthetic magnetic field deep in the quantum Hall regime. The erbium atom, with a non-vanishing orbital angular momentum in the electronic ground state, allows for state-dependent optical manipulation with large detuning of the driving optical field, and correspondingly strong synthetic gauge fields at long coher-ence times. We will investigate the synthesis of magnetic fields for the cold rare earth atomic quantum gas and study fractional quantum Hall-type states. Within the first grant period, we will focus onto the use of bosonic isotopes of the erbium atomic system in synthetic gauge fields. Evidence for the correlated multiparticle regime can be obtained from the observation of collapse and revival of the interference pattern of the two-dimensional atomic microclouds in the strong synthetic magnetic field. In this way novel perspectives arise for the generation of fractional quantum Hall states, providing an atomic physics analog to two-dimensional electron gases. Relying on the unusual electronic properties of rare earth atoms, we will investi-gate novel states of matter with nontrivial topology, beyond the mean field quantum Hall regime. Perspectives of this work are the observation of anyonic statistics of excitations, which is predicted for such two-dimensional atomic microclouds subject to a strong synthetic magnetic field deep in the quantum Hall regime, and the investigation of the coupling of the topological states to reservoirs.