Topological Phase Transitions and Thouless Pumping of Light in Photonic Waveguide Arrays

TL;DR

This paper investigates topological phase transitions and Thouless pumping in photonic waveguide arrays, providing a method to measure bulk topological invariants and revealing nontrivial topological phases with large Chern numbers.

Contribution

It constructs a topological phase diagram for commensurate AAH photonic arrays and proposes a scheme to measure bulk Chern numbers via Thouless pumping.

Findings

Identification of nontrivial topological phases with large Chern numbers

Demonstration of bulk-edge correspondence in photonic systems

Proposal of a scheme to measure bulk Chern numbers through light pumping

Abstract

Photonic waveguide arrays provide an excellent platform for simulating conventional topological systems, and they can also be employed for the study of novel topological phases in photonics systems. However, a direct measurement of bulk topological invariants remains a great challenge. Here we study topological features of generalized commensurate Aubry-Andr\'{e}-Harper (AAH) photonic waveguide arrays and construct a topological phase diagram by calculating all bulk Chern numbers, and then explore the bulk-edge correspondence by analyzing the topological edge states and their winding numbers. In contrast to incommensurate AAH models, diagonal and off-diagonal commensurate AAH models are not topologically equivalent. In particular, there appear nontrivial topological phases with large Chern numbers and topological phase transitions. By implementing Thouless pumping of light in photonic waveguide arrays, we propose a simple scheme to measure the bulk Chern numbers.