Probing the topological phase transition in the Su-Schrieffer-Heeger Hamiltonian using Rydberg-atom synthetic dimensions

We experimentally investigate the Su-Schrieffer-Heeger (SSH) Hamiltonian using Rydberg-atom synthetic dimensions constructed, in a single atom, from a ladder of six neighboring $n\phantom{\rule{0.222222em}{0ex}}^{3}S_{1}$ Rydberg states in which adjacent states are coupled with two-photon transitions using microwave fields. Alternating strong or weak tunneling rates, controlled by adjusting the microwave amplitudes, are varied to explore the topological phase transition inherent in the SSH Hamiltonian as a function of the ratio of the tunneling rates. For each ratio, quench dynamics experiments, in which the system is initially prepared in one of the bulk Rydberg states and then subjected to the microwave fields, are performed to measure the population evolution of the system. From the dynamics measurements, we extract the mean chiral displacement and verify that its long-time average value converges towards the system winding number. The loss of nontrivial topology is also examined by probing the energy spectrum of the system in steady state and observing the disappearance of the zero-energy edge states. The results show that even a system with as few as six levels can demonstrate the essential characteristics of the SSH Hamiltonian.