Realizing Su-Schrieffer-Heeger topological edge states in Rydberg-atom synthetic dimensions

Synthetic dimensions based on coupled Rydberg levels in ultracold atoms can be a powerful tool for quantum simulation. We demonstrate this platform by implementing the Su-Schrieffer-Heeger (SSH) Hamiltonian on a Rydberg strontium atom. The Rydberg levels are interpreted as synthetic lattice sites and the tunneling is introduced through resonant millimeter-wave couplings. The millimeter-wave amplitudes control the tunneling amplitudes whereas frequency detunings of the millimeter waves from resonance control the on-site potential. We attain a configuration with symmetry-protected topological edge states by using an alternating weak and strong tunneling pattern, with weak tunneling to edge lattice sites. The band structure is probed through optical excitation to the Rydberg levels from the ground state, which reveals topological edge states at zero energy. We verify that edge-state energies are robust to perturbation of tunneling-rates, which preserves chiral symmetry, but can be shifted by the introduction of on-site potentials. The scope of Rydberg-atom synthetic dimensions in realizing higher dimensional systems, non-trivial spatial and band structure topologies, artificial gauge fields and many-body physics with long-range interactions in optical tweezers will also be discussed.

This research was supported by the AFOSR (FA9550-17-1-0366), NSF (PHY-1904294 and PHY-1848304), and the Robert A. Welch Foundation (C0734, C-1844, and C-1872).