Topological Inverse Band Theory in Waveguide Quantum Electrodynamics

Area of Science:

• Quantum physics
• Topological matter
• Light-matter interactions

Background:

• Topological phases are vital in quantum technologies and light-matter interactions.
• Existing topological band theory fails in waveguide quantum electrodynamics (QED) systems due to disconnected energy bands.

Purpose of the Study:

• Introduce the concept of inverse energy bands.
• Analytically explore topological scattering in waveguide systems with quantum emitters.
• Investigate topological phase transitions and associated phenomena.

Main Methods:

• Analytical exploration of topological scattering.
• Development and application of the inverse energy band concept.
• Investigation of waveguide quantum electrodynamics systems with quantum emitters.

Main Results:

• Uncovered topological phase transitions, scale-free localization, and flat bands.
• Identified dark Wannier states.
• Demonstrated that scale-free localized states reside in inverse energy bands, with distribution varying between topological and trivial phases.
• Found that winding number depends on the inverse subradiant band's topological phase and cell number parity.

Conclusions:

• The study establishes the field of topological inverse bands.
• Introduces a novel perspective on topological phases in light-matter interactions.
• Highlights the breakdown and subsequent redefinition of bulk-edge correspondence in the presence of radiative decay.