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

The cooperative modification of spontaneous radiative decay is a paradigmatic many-emitter effect in quantum optics. So far its experimental realization has involved interactions mediated by rapidly escaping photons that do not play an active role in the emitter dynamics. Here we explore cooperative dynamics of quantum emitters in an optical lattice that interact by radiating atomic matter waves. Using the ability to prepare weakly and strongly interacting many-body phases of excitations in an array of matter-wave emitters, we demonstrate directional super- and subradiance from a superfluid phase with tunable radiative phase lags, and directly access the buildup of coherence imprinted by the emitted radiation across a Mott insulator. We investigate the onset of cooperative dynamics for slow wave propagation and observe a coupling to collective bound states with radiation trapped at and between the emitters. Our results in open-system quantum electrodynamics establish ultracold matter waves as a versatile tool for studying many-body quantum optics in spatially extended and ordered systems.