Propagation in media as a probe for topological properties

TL;DR

This thesis develops experimental methods using cold atoms in optical lattices to study and identify topological phases, focusing on constructing bound states and measuring topological invariants directly from atomic dynamics.

Contribution

It introduces novel techniques for probing topological properties in quantum systems, including methods to identify protected states and measure invariants in low-dimensional systems.

Findings

Identification of topologically protected bound states in 1D chiral systems

Direct measurement of topological invariants in 2D Hofstadter strips

Advancement in experimental approaches for topological phase classification

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.