The Vienna Doctoral Programme on Complex Quantum Systems invites to a Students TALK by Guiseppe Calajo Atom-field dressed states in slow-light waveguide QED We discuss the properties of atom-photon bound states in waveguide QED systems consisting of single or multiple atoms coupled strongly to a finite-bandwidth photonic channel. Such bound states are formed by an atom and a localized photonic excitations and represent the continuum analog of the familiar dressed states in single-mode cavity QED. In this work we present a detailed analysis of the linear and nonlinear spectral features associated with singleand multi-photon dressed states and show how the formation of bound states affects the waveguide-mediated dipole-dipole interactions between separated atoms. Our results provide a both qualitative and quantitative description of the essential strong-coupling processes in waveguide QED systems, which are currently developed in the optical and the microwave regime.