Topological inverse band theory in waveguide quantum electrodynamics

TL;DR

This paper introduces the concept of inverse energy bands in waveguide QED systems, revealing topological phase transitions, localized states, and novel topological properties despite the breakdown of traditional bulk-edge correspondence.

Contribution

It develops the theory of topological inverse bands in waveguide QED, uncovering new topological phenomena and states not explained by conventional band theory.

Findings

Discovery of topological phase transitions in inverse bands

Identification of scale-free localized dark states

Analytical proof of topological properties in inverse bands

Abstract

Topological phases play a crucial role in the fundamental physics of light-matter interaction and emerging applications of quantum technologies. However, the topological band theory of waveguide QED systems is known to break down, because the energy bands become disconnected. Here, we introduce a concept of the inverse energy band and explore analytically topological scattering in a waveguide with an array of quantum emitters. We uncover a rich structure of topological phase transitions, symmetric scale-free localization, completely flat bands, and the corresponding dark Wannier states. Although bulk-edge correspondence is partially broken because of radiative decay, we prove analytically that the scale-free localized states are distributed in a single inverse energy band in the topological phase and in two inverse bands in the trivial phase. Surprisingly, the winding number of the scattering textures depends on both the topological phase of inverse subradiant band and the odevity of the cell number. Our work uncovers the field of the topological inverse bands, and it brings a novel vision to topological phases in light-matter interactions.