[Paper Review] Realizing Su-Schrieffer-Heeger topological edge states in Rydberg-atom synthetic dimensions

S. K. Kanungo, J. D. Whalen+6 more|arXiv (Cornell University)|Jan 8, 2021

Cold Atom Physics and Bose-Einstein Condensates1 references4 citations

TL;DR

This paper demonstrates a synthetic dimension in ultracold 84Sr atoms using Rydberg levels coupled by millimeter-wave fields, realizing the Su-Schrieffer-Heeger (SSH) model with tunable tunneling and on-site potentials. Topological edge states emerge at zero energy in the band gap, confirmed by optical excitation and robust against chiral-symmetry-preserving perturbations, validating the platform for simulating topological quantum matter.

ABSTRACT

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.

Motivation & Objective

• To create a synthetic dimension using Rydberg levels in ultracold 84Sr atoms for quantum simulation of topological phases.
• To implement the Su-Schrieffer-Heeger (SSH) Hamiltonian with tunable tunneling and on-site potentials using resonant millimeter-wave couplings.
• To observe symmetry-protected topological edge states in a synthetic 1D lattice and verify their robustness to perturbations.

Proposed method

• Rydberg levels (ns and np states) of 84Sr are used as synthetic lattice sites, with tunneling induced by near-resonant millimeter-wave fields.
• Tunneling amplitudes are controlled via millimeter-wave Rabi frequencies, while on-site potentials are tuned via detuning from resonance.
• The SSH model is realized with alternating weak and strong tunneling, where edge sites are coupled with weaker tunneling to induce topological edge states.
• Band structure and eigenstate populations are probed via optical excitation to Rydberg levels, with site-resolved detection using spatially resolved fluorescence imaging (SFI).
• Perturbations to tunneling rates and on-site potentials are applied to test chiral symmetry and edge state robustness.

Experimental results

Research questions

• RQ1 Can Rydberg levels in ultracold atoms be used to realize a synthetic dimension with tunable tunneling and on-site potentials?
• RQ2 Does the SSH model with alternating tunneling in a synthetic 1D lattice support topologically protected edge states?
• RQ3 Are the energies of these edge states robust under chiral-symmetry-preserving perturbations?
• RQ4 How do on-site potential shifts affect edge state energies, and can this be used to probe localization?
• RQ5 Can the platform resolve individual lattice-site populations and confirm edge state localization?

Key findings

• Topological edge states were observed at zero energy in the band gap of the six-site SSH model, confirmed by optical excitation spectra.
• The edge state energy remains at zero when tunneling rates are imbalanced in a chiral-symmetry-preserving manner, demonstrating robustness.
• When chiral symmetry is broken by detuning the millimeter-wave coupling to the i=1 (57s) site, the edge state energy shifts by an amount equal to the detuning.
• The orthogonal edge state, localized on the i=6 (59p) site, remains unaffected when the i=1 coupling is detuned, confirming site-specific localization.
• Spatially resolved fluorescence imaging (SFI) with two-site resolution confirms the decomposition of eigenstates and validates the lattice eigenstate populations.