Spin Many-Body Phases in Standard- and Topological-Waveguide QED Simulators

Waveguide QED has emerged as a powerful analog quantum simulator due to the possibility of mediating versatile spin-spin interactions with tunable sign, range, and even dimerization. Yet, despite their potential, the many-body phases emerging from these systems have only been scarcely explored. Here, we characterize the many-body phases of a large class of spin models that can be obtained in such waveguide-QED simulators and uncover, importantly, the existence of symmetry-protected topological phases with large-period magnetic orderings with no analog in other state-of-art simulators. We explain that these phases emerge from the unique combination of long-range and dimerized interactions appearing in these platforms and propose several experimental observables to characterize them. Finally, we also develop an adiabatic protocol to prepare such states and analyze its performance with the main decoherence source of these systems.