Solving for the dynamics of many-body quantum systems is typically hard, unless there is a high degree of symmetry present. An example of the latter in the context of quantum optics is Dicke superradiance, where excited atoms self-organize as they decay, emitting a short and intense pulse of light. While well understood in a cavity, the problem of many-body decay in extended systems remains open, due to the exponential growth of complexity with atom number. In this talk, I will discuss how coherent behavior emerges in extended quantum systems, and how to understand the dynamics in atomic arrays without the need of heavy computation. Our analytical results provide insights on the critical role of dimensionality on the many-body dynamics, as well as point to universal behavior that is lattice-geometry independent. Our predictions can be tested in state of the art experiments with arrays of neutral atoms, and pave the way towards understanding the role of many-body decay in extended systems for metrology and lasing.
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