Quantum tunnelling

Quantum mechanics

Optical lattice

Rydberg atom

Superfluidity

Rydberg formula

Atomic physics

Excitation

Mathematical optimization

Hamiltonian (control theory)

Ultracold atom

Rydberg state

Physics

Ionization

Amplitude

Mathematics

Point reflection

Condensed matter physics

Quantum

Combinatorics

Wave function

Topology (electrical circuits)

Nature Communications

We demonstrate a platform for synthetic dimensions based on coupled Rydberg levels in ultracold atoms, and we implement the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian. Rydberg levels are interpreted as synthetic lattice sites, with tunneling introduced through resonant millimeter-wave couplings. Tunneling amplitudes are controlled through the millimeter-wave amplitudes, and on-site potentials are controlled through detunings of the millimeter waves from resonance. Using alternating weak and strong tunneling with weak tunneling to edge lattice sites, we attain a configuration with symmetry-protected topological edge states. 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.

Realizing topological edge states with Rydberg-atom synthetic dimensions