Quasi-degenerate resonant eigenstate doublets of two quantum emitters in a closed waveguide

TL;DR

This paper explores the conditions under which pairs of quantum emitters in a finite waveguide form quasi-degenerate eigenstate doublets, enabling potential applications in quantum technology through controlled photon confinement.

Contribution

It demonstrates the existence of quasi-degenerate resonant doublets in a finite waveguide system, revealing new ways to manipulate emitter-waveguide interactions for quantum applications.

Findings

Identification of conditions for quasi-degenerate doublets

Doublets remain well separated near degeneracy points

Potential for effective two-level system manipulation

Abstract

The physics of systems of quantum emitters in waveguide quantum electrodynamics is significantly influenced by the relation between their spatial separation and the wavelength of the emitted photons. If the distance that separates a pair of emitters meets specific resonance conditions, the photon amplitudes produced from decay may destructively interfere. In an infinite-waveguide setting, this effect gives rise to bound states in the continuum, where a photon remains confined between the emitters. In the case of a finite-length waveguide with periodic boundary conditions, there exist two such relevant distances for a given arrangement of the quantum emitters, leading to states in which a photon is confined to either the shorter or the longer path that connects the emitters. If the ratio of the shorter and the longer path is a rational number, these two kinds of resonant eigenstates are allowed to co-exist for the same Hamiltonian. In this paper, we investigate the existence of quasi-degenerate resonant doublets of a pair of identical emitters coupled to a linear waveguide mode. The states that form the doublet are searched among the ones in which a single excitation tends to remain bound to the emitters. We investigate the spectrum in a finite range around degeneracy points to check whether the doublet remains well separated from the closest eigenvalues in the spectrum. The identification of quasi-degenerate doublets opens the possibility to manipulate the emitters-waveguide system as an effectively two-level system in specific energy ranges, providing an innovative tool for quantum technology tasks.