Photonic Bound States and Scattering Resonances in Waveguide QED

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.

6+1 pages, 4 figures

References in corpus (8)

• Chiral Quantum Optics
• Strongly Correlated Two-Photon Transport in One-Dimensional Waveguide Coupled to A Two-Level System
• Nonlinear response of the vacuum Rabi resonance
• Strongly-correlated multi-particle transport in one-dimension through a quantum impurity: an outline of exact and complete solutions
• Strongly correlated states of light in chiral chains of three-level quantum emitters
• Quantum Hall phase emerging in an array of atoms interacting with photons
• Radiative topological biphoton states in modulated qubit arrays
• Waveguide quantum optomechanics: parity-time phase transitions in ultrastrong coupling regime