"A quantum system evolving on a manifold of discrete states can be viewed as a particle moving in a real-space lattice potential. Such a synthetic dimension provides a powerful tool for quantum simulation because of the ability to engineer many aspects of the Hamiltonian describing the system. In this talk, I will describe a synthetic dimension created from Rydberg levels in an 84-Sr atom, in which coupling between the states is induced with millimeter-waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger Hamiltonian, a paradigmatic model of topological matter. I will also briefly describe our recent results creating ultralong-range Rydberg molecule (ULRRM) dimers in an interacting Bose gas and probing nonlocal three-body spatial correlations with ULRRM trimers.
Kanungo, S.K., Whalen, J.D., Lu, Y. et al. Realizing topological edge states with Rydberg-atom synthetic dimensions. Nat Commun 13, 972 (2022). https://doi.org/10.1038/s41467-022-28550-y