Combinatorics

Physics

Topology (electrical circuits)

Point reflection

Mathematics

Rydberg atom

Quantum tunnelling

Mathematical optimization

Ultracold atom

Wave function

Hamiltonian (control theory)

Atomic physics

Superfluidity

Amplitude

Ionization

Condensed matter physics

Rydberg state

Quantum mechanics

Rydberg formula

Excitation

Quantum

Optical lattice

Nature Communications

A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold 84Sr atom, we demonstrate a synthetic-dimension based on Rydberg levels coupled 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 (SSH) Hamiltonian, a paradigmatic model of topological matter. Band structure is probed through optical excitation from the ground state to Rydberg levels, revealing symmetry-protected topological edge states at zero energy. Edge-state energies are robust to perturbations of tunneling-rates that preserve chiral symmetry, but can be shifted by the introduction of on-site potentials.

Realizing topological edge states with Rydberg-atom synthetic dimensions