Generation of single and two-mode multiphoton states in waveguide QED

Single and two-mode multiphoton states are the cornerstone of many quantum technologies, e.g., metrology. In the optical regime these states are generally obtained combining heralded single-photons with linear optics tools and post-selection, leading to inherent low success probabilities. In a recent paper, we design several protocols that harness the long-range atomic interactions induced in waveguide QED to improve fidelities and protocols of single-mode multiphoton emission. Here, we give full details of these protocols, revisit them to simplify some of their requirements and also extend them to generate two-mode multiphoton states, such as Yurke or NOON states.