Probing topological edge states in a molecular synthetic dimension

Abstract Synthetic dimensions, where additional spatial dimensions are encoded within the internal states of a quantum system, allow the realisation of phenomena usually inaccessible in experiments. Ultracold polar molecules are an ideal platform for synthetic dimensions, providing large Hilbert spaces of long-lived rotational and hyperfine states that can be linked with microwave fields to simulate tunnelling. Here, we realise a one-dimensional synthetic lattice using the rotational states of ultracold RbCs molecules and investigate the topological properties of the Su-Schrieffer-Heeger model. We spectroscopically probe the system using an auxiliary rotational state and study the time dynamics after deterministic state preparation. We demonstrate long coherence times, reaching ~ 500 tunnelling periods even for lattices spanning eight rotational states. Using full site-resolved readout over long evolution times, we study the robustness of topologically protected edge states against perturbations that preserve or break chiral symmetry. These results establish ultracold molecules as a powerful platform for quantum simulation using synthetic dimensions.