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The cooperative modification of spontaneous radiative decay is a paradigmaticmany-emitter effect in quantum optics. So far its experimental realization hasinvolved interactions mediated by rapidly escaping photons that do not play anactive role in the emitter dynamics. Here we explore cooperative dynamics ofquantum emitters in an optical lattice that interact by radiating atomic matterwaves. Using the ability to prepare weakly and strongly interacting many-bodyphases of excitations in an array of matter-wave emitters, we demonstratedirectional super- and subradiance from a superfluid phase with tunableradiative phase lags, and directly access the buildup of coherence imprinted bythe emitted radiation across a Mott insulator. We investigate the onset ofcooperative dynamics for slow wave propagation and observe a coupling tocollective bound states with radiation trapped at and between the emitters. Ourresults in open-system quantum electrodynamics establish ultracold matter wavesas a versatile tool for studying many-body quantum optics in spatially extendedand ordered systems.

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