Probing the topological phase transition in the Su-Schrieffer-Heeger model using Rydberg-atom synthetic dimensions

TL;DR

This study uses Rydberg-atom synthetic dimensions to simulate the SSH model, demonstrating the topological phase transition through quench dynamics and spectral analysis in a minimal six-level system.

Contribution

It introduces a novel experimental platform for simulating topological phases using Rydberg atoms with synthetic dimensions, enabling direct observation of phase transition signatures.

Findings

Verification of the topological phase transition via mean chiral displacement.

Observation of zero-energy edge state disappearance at the transition.

Demonstration that a six-level system captures key SSH characteristics.

Abstract

We simulate the the Su-Schrieffer-Heeger (SSH) model using Rydberg-atom synthetic dimensions constructed, in a single atom, from a ladder of six neighboring $n\:^3S_1$ Rydberg states in which adjacent states are coupled with two-photon transitions using microwave fields. Alternating strong/weak tunneling rates, controlled by adjusting the microwave amplitudes, are varied to map out the topological phase transition as a function of the ratio of the tunneling rates. For each ratio, quench dynamics experiments, in which the system is initially prepared in one of the bulk Rydberg states and then subjected to the microwave fields, are performed to measure the population evolution of the system. From the dynamics measurements, we extract the mean chiral displacement and verify that its long-time average value converges towards the system winding number. The topological phase transition is also examined by probing the energy spectrum of the system in steady state and observing the disappearance of the zero-energy edge states. The results show that even a system with as few as six levels can demonstrate the essential characteristics of the SSH Hamiltonian.