Bound, antibound and resonance two-photon states in chiral waveguide QED

TL;DR

This paper provides a comprehensive theoretical analysis of two-photon states in chiral waveguide QED, revealing bound, antibound, and resonance states across all momentum values and highlighting a gapless spectrum with topological features.

Contribution

It introduces a complete spectrum analysis for two-particle states in chiral waveguide QED, including bound and resonance states over all momentum ranges, and discusses topological effects.

Findings

Existence of bound, antibound, and resonance states for all momentum values.

The spectrum is gapless and consistent across all center-of-mass momenta.

The dispersion law indicates a topological non-Hermitian skin effect.

Abstract

We present a theoretical study of the two-particle spectrum $\omega(K)$ for the chiral waveguide QED setup of an array of two-level atoms directionally interacting with photons propagating along the waveguide. We demonstrate that for each pair center-of-mass momentum $K$ there exist distinct solutions with $\Im\omega\le 0$ in the two-particle spectrum, corresponding to bound, antibound and resonance states, in addition to the continuum of scattering states. Contrary to previous studies, which showed the bound and resonance-state spectra only over a limited range of $K$, the calculated spectrum is consistent across all $K$ values. An interesting finding is that the real part of the spectrum $\Re \omega(K)$ in the chiral model is gapless. The calculated dispersion law $\omega(K)$ provides an effective model for the bound photon pairs also in a finite-size array, manifesting the topological non-Hermitian skin effect.