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Waveguide quantum electrodynamics constitutes a modern paradigm for the interaction of light and matter, in which strong coupling, bath structure, and propagation delays can break the radiative conditions that quantum emitters typically encounter in free space. These characteristics intertwine the excitations of quantum emitters and guided radiation modes to form complex multiphoton dynamics. So far, combining the collective decay of the emitters with the non-Markovian effects induced by the modes has escaped a full solution and the detailed physics behind these systems remains unknown. Here we analyze such a collective non-Markovian decay in a minimal system of two excited emitters coupled to a one-dimensional single-band waveguide. We develop an exact solution for this system in terms of elementary functions that unveils hidden symmetries and predicts new forms of spontaneous decay. The collective non-Markovian dynamics, which are strongly dependent on the vacuum coupling and the detuning from the center of the band, show exotic features that can be characterized with a simple and readily available criterion. Our analytic methods shed light on the complexity of collective light-matter interactions and open up a pathway for understanding multiparticle open quantum systems. Published by the American Physical Society2024 

The cooperative modification of spontaneous radiative decay exemplifies a many-emitter effect in quantum optics. So far, its experimental realizations have relied on interactions mediated by rapidly escaping photons, which do not play an active role in the emitter dynamics. Here we use a platform of ultracold atoms in a one-dimensional optical lattice geometry to explore cooperative non-Markovian dynamics of synthetic quantum emitters that decay by radiating slow atomic matter waves. By preparing and manipulating arrays of emitters hosting weakly and strongly interacting many-body phases of excitations, we demonstrate directional collective emission and study the interplay between retardation and super- and subradiant dynamics. Moreover, we directly observe the spontaneous buildup of coherence among emitters. Our results on collective radiative dynamics establish ultracold matter waves as a versatile tool for studying many-body quantum optics in spatially extended and ordered systems.