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

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 $\mathrm{\Im }\omega \le 0$ 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 $\mathrm{\Re }\omega (K)$ 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.