2D Topological Chiral Edge-States in a Synthetic Dimension of Atomic Trap States

Given the broad interest in topological physics, many powerful tools have been developed to induce such effects in a plethora of platforms, like cold atoms. One such technique is that of "synthetic dimensions", in which a set of states is externally coupled to engineer an effective spatial dimension. This approach is well-suited to investigating topological systems as the external coupling can naturally be designed to imprint a desired artificial magnetic field, and hence engineer quantum Hall-like models. In Birmingham, we have been developing a type of synthetic dimension that is based on coupling the harmonic trap states associated with cold atomic clouds. To first test this platform, a recent experiment demonstrated 1D Bloch oscillations along the synthetic dimension. We now theoretically propose how to realise a 2D quantum Hall system in this set-up by combining the synthetic dimension with a real spatial dimension and an artificial magnetic field. We demonstrate how to induce topological one-way chiral orbits with experimentally realistic parameters. We highlight, through numerical investigation, how to tune the length and add impurities to the synthetic dimension by using a digital micro-mirror device. Additionally, we utilise the length of the synthetic dimension to investigate bulk physics, specifically cyclotron orbits. This opens the way for future experiments on quantum Hall physics with atomic trap states.