Topological phases with Rydberg atoms*

The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. In this talk, we review  different approaches for the realization of topological phases with Rydberg atoms. Starting with the recent experimental observation of a symmetry protected topological phase, we extend the approaches into two dimensions on fractional bosonic Chern insulators.  The required experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.