Heralded multiphoton states with coherent spin interactions in waveguide QED

Waveguide QED offers the possibility of generating strong coherent atomic interactions either through appropriate atomic configurations in the dissipative regime or in the bandgap regime. In this work, we show how to harness these interactions in order to herald the generation of highly entangled atomic states, which afterwards can be mapped to generate single mode multi-photonic states with high fidelities. We introduce two protocols for the preparation of the atomic states, we discuss their performance and compare them to previous proposals. In particular, we show that one of them reaches high probability of success for systems with many atoms but low Purcell factors.