Measuring $\mathbb{Z}_2$ invariants in dimer models and cross-coupled ladders with a programmable photonic molecule

TL;DR

This paper demonstrates the experimental realization of topological 1-D lattice models using fiber ring resonators, introducing a novel low-noise measurement technique for topological invariants and extending to ladder models with complex flux configurations.

Contribution

It introduces cascaded heterodyning for single-shot topological invariant measurement and extends fiber optics platforms to simulate complex ladder models with flux.

Findings

Successful measurement of winding numbers using heterodyning

Realization of a modified Creutz ladder with staggered flux

Extension of fiber resonator platform to complex topological models

Abstract

Topological models are characterized by a quantized topological invariant and provide a description of novel phases of matter that can exhibit localized edge states, corner modes, and chiral transport. We experimentally realize two 1-D lattices supporting symmetry-protected topology - the Su-Schrieffer-Heeger (SSH) and extended SSH models using the synthetic frequency dimension of coupled fiber ring resonators. We introduce and experimentally demonstrate cascaded heterodyning as a technique for low-noise, single-shot winding number measurements through the mean chiral displacement and band structure measurements. Through our robust setup and detection techniques we can extend our capability to realizing 1-D ladder models, demonstrating a modified Creutz ladder with a staggered flux with each plaquette. This highly reconfigurable and compact fiber optics platform for Hamiltonian simulation, along with a low-noise detection scheme, provides a path forward for chip-scale realizations.