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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.