Realizing topological edge states with Rydberg-atom synthetic dimensions

S K Kanungo; J D Whalen; Y Lu; M Yuan; S Dasgupta; F B Dunning; K R A Hazzard; T C Killian

doi:10.1038/s41467-022-28550-y

Realizing topological edge states with Rydberg-atom synthetic dimensions

Nat Commun. 2022 Feb 21;13(1):972. doi: 10.1038/s41467-022-28550-y.

Authors

S K Kanungo^{1

2}, J D Whalen^{3

4}, Y Lu^{3

4}, M Yuan^{3

4

5

6}, S Dasgupta^{3

4}, F B Dunning³, K R A Hazzard^{7

8}, T C Killian^{9

10}

Affiliations

¹ Department of Physics and Astronomy, Rice University, Houston, TX, 77005-1892, USA. skk4@rice.edu.
² Rice Center for Quantum Materials, Rice University, Houston, TX, 77005-1892, USA. skk4@rice.edu.
³ Department of Physics and Astronomy, Rice University, Houston, TX, 77005-1892, USA.
⁴ Rice Center for Quantum Materials, Rice University, Houston, TX, 77005-1892, USA.
⁵ School of the Gifted Young, University of Science and Technology of China, Hefei, 230026, China.
⁶ Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, 60637, USA.
⁷ Department of Physics and Astronomy, Rice University, Houston, TX, 77005-1892, USA. kaden@rice.edu.
⁸ Rice Center for Quantum Materials, Rice University, Houston, TX, 77005-1892, USA. kaden@rice.edu.
⁹ Department of Physics and Astronomy, Rice University, Houston, TX, 77005-1892, USA. killian@rice.edu.
¹⁰ Rice Center for Quantum Materials, Rice University, Houston, TX, 77005-1892, USA. killian@rice.edu.

Abstract

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.