Dicke superradiance requires interactions beyond nearest-neighbors

It is well known that the photon interactions within an excited ensemble of emitters can result in Dicke superradiance, where the emission rate is greatly enhanced, manifesting as a high-intensity burst at short times. For ordered arrays, superradiant burst is most commonly observed in systems with long-range interactions between the emitters, although the minimal interaction range remains unknown. In this work, we prove that for an arbitrary emitter array with only nearest-neighbor interactions in all dimensions, superradiant burst violates the positivity of the density matrix and is thus not physically observable. We show that superradiance requires minimally the inclusion of next-nearest-neighbor interactions. For exponentially-decaying interactions, the critical coupling was found to be asymptotically independent of the number of emitters in all dimensions, thereby defining the threshold interaction range where the collective enhancement balances out the decoherence effects. Our findings provide key physical insights to the understanding of collective decay in many-body quantum systems, and the designing of superradiant emission in physical systems for applications such as energy harvesting and quantum sensing.