Photonic Bound States and Scattering Resonances in Waveguide QED

TL;DR

This paper analytically investigates two-photon bound states and scattering resonances in waveguide QED systems with chiral properties, revealing their dispersion, internal structure, and decay dynamics.

Contribution

It introduces a systematic analytical method to determine two-photon eigenstates in waveguide QED with chiral emitter arrays, identifying bound states and resonances.

Findings

Identification of two types of two-photon bound states

Derivation of their dispersion relations and internal structures

Discovery of long-lived bound states and decaying scattering resonances

Abstract

We study the emergence of two types of two-photon bounds states in waveguides of any chirality. Specifically, we present a systematic way of analytically determining the eigenstates of a system consisting of a waveguide coupled to a partially chiral, infinite array of equidistant two-level emitters. Using an effective Hamiltonian approach, we determine the properties of the two-photon bound states by determining their dispersion relation and internal structure. The bound states come in two varieties, depending on the two-photon momentum and emitter spacing. One of these states is a long-lived true bound state, whereas the other, a scattering resonance, decays in time via coupling to free two-photon states, leading to resonances and corresponding phase shifts in the photon-photon scattering.