Title: Propagation in media as a probe for topological properties,
Abstract: The central goal of this thesis is to develop methods to experimentally study
topological phases. We do so by applying the powerful toolbox of quantum
simulation techniques with cold atoms in optical lattices. To this day, a
complete classification of topological phases remains elusive. In this context,
experimental studies are key, both for studying the interplay between topology
and complex effects and for identifying new forms of topological order. It is
therefore crucial to find complementary means to measure topological properties
in order to reach a fundamental understanding of topological phases. In one
dimensional chiral systems, we suggest a new way to construct and identify
topologically protected bound states, which are the smoking gun of these
materials. In two dimensional Hofstadter strips (i.e: systems which are very
short along one dimension), we suggest a new way to measure the topological
invariant directly from the atomic dynamics.