Super- and subradiant dynamics of quantum emitters mediated by atomic matter waves

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.