Realizing topological edge states with Rydberg-atom synthetic dimensions

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

doi:10.1038/s41467-022-28550-y

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.

Highlights

A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential
The essential elements of the apparatus are shown in Fig. 1a. 84Sr atoms are trapped in an optical dipole trap at a peak density of about 1011 cm−3 and a temperature of T = 2 μK
The kets jii correspond to the unperturbed Rydberg levels of 84Sr up to a time-dependent phase arising from the transformation

Summary

Introduction

A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Synthetic dimensions are powerful tools for quantum simulation, opening exciting possibilities such as the realization of higher dimensional systems[1,3,4], non-trivial real space[5,6] and band structure[7,8] topologies, and artificial gauge fields[9,10]. These can be used in conjunction with real space lattices to create situations unavailable to either method individually. The concept of a synthetic dimension was recently used to explain conical intersections in the potential energy curves of Rydberg molecules[31]

Methods

Results

Conclusion