  We simulate the the Su-Schrieffer-Heeger (SSH) model using Rydberg-atom
synthetic dimensions constructed, in a single atom, from a ladder of six
neighboring $n\:^3S_1$ Rydberg states in which adjacent states are coupled with
two-photon transitions using microwave fields. Alternating strong/weak
tunneling rates, controlled by adjusting the microwave amplitudes, are varied
to map out the topological phase transition 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 topological phase transition 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.
