Decoherence is ubiquitous in quantum physics, from the conceptual foundations [1] to quantum information processing or quantum technologies, where it is a threat that must be countered. While decoherence has been extensively studied for simple, well-isolated systems such as single atoms or ions [2], much less is known for manybody systems where inter-particle correlations and interactions can drastically alter the dissipative dynamics [3][4][5][6]. Here we report an experimental study of how spontaneous emission destroys the spatial coherence of a gas of strongly interacting bosons in an optical lattice. Instead of the standard momentum diffusion expected for independent atoms [7], we observe an anomalous sub-diffusive expansion, associated with a universal slowing down ∝ 1/t 1/2 of the decoherence dynamics. This algebraic decay reflects the emergence of slowly-relaxing many-body states [5], akin to sub-radiant states of many excited emitters [4]. These results, supported by theoretical predictions, provide an important benchmark in the understanding of open many-body systems.Interference phenomena are a central feature of quantum mechanics. However, they are easily destroyed by uncontrolled couplings with the environment, i.e. decoherence. In weakly correlated systems, inter-particle interactions are typically expected to hasten decoherence. For instance, they are responsible for the collisional broadening of spectral lines in hot atomic vapors. For strongly interacting many-body systems, the theory of non-equilibrium dynamics in general and of decoherence in particular remains challenging, and experiments can provide valuable insight. Improving our understanding of such problems could also help developing novel experimental methods harnessing dissipation to engineer specific quantum states [8].Ultracold atoms provide a natural experimental platform to investigate these questions. Coherence of ultracold quantum gases is usually easily accessible experimentally, and the sources of relaxation are often well identified and experimentally controllable. Along these lines, experiments with dissipative atomic quantum gases have so far mainly explored the role of atom losses, demonstrating variants of the Zeno effect [9-13], bi-stability of transport [14] or loss cooling [15,16]. Spontaneous emission provides a different dissipation mechanism. An atom excited by a near-resonant laser under-goes repeated photon absorption-spontaneous emission cycles. The atomic momentum changes randomly after each spontaneous emission and undergoes a random walk in momentum space with a width asymptotically scaling as ∆p ∝ √ t [6,7]. This momentum diffusion, well-known in the context of laser cooling [17,18], suppresses interferences between different parts of the system, as observed in the pioneering experiment of [19]. The destruction of spatial coherence was also observed indirectly through the inhibition of tunneling for a dilute normal gas in an optical lattice [20], where interactions do not play any role. In addition, the impact o...