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

This is the authors' abstract. We don't add key points for this paper.

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 [A. Gonz\'alez-Tudela et al., Phys. Rev. Lett. 118, 213601 (2017)], 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.