Photon-mediated 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. The superradiant burst is most commonly observed in systems with long-range interactions between the emitters, although the minimal interaction range remains unknown. Here, we put forward a new theoretical method to bound the maximum emission rate by upper bounding the spectral radius of an auxiliary Hamiltonian. We harness this tool to prove that for an arbitrary ordered array with only nearest-neighbor interactions in all dimensions, a superradiant burst is not physically observable. We show that Dicke superradiance requires minimally the inclusion of next-nearest-neighbor interactions. For exponentially decaying interactions, the critical coupling is 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.

中文翻译：

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Dicke Superradiance 需要超越最近邻的相互作用

在激发的发射器集合中，光子介导的相互作用可以导致 Dicke 超辐射，其中发射率大大提高，表现为短时间内的高强度爆发。超辐射爆发最常在发射器之间具有远程相互作用的系统中观察到，尽管最小的相互作用范围仍然未知。在这里，我们提出了一种新的理论方法，通过上限辅助哈密顿量的光谱半径来限制最大发射率。我们利用这个工具来证明，对于在所有维度上只有最近邻相互作用的任意有序阵列，超辐射爆发在物理上是不可观察的。我们表明，Dicke 超辐射至少需要包含下一个最近邻相互作用。对于指数衰减的相互作用，发现临界耦合渐近独立于所有维度的发射器数量，从而定义了集体增强平衡退相干效应的阈值交互范围。我们的研究结果为理解多体量子系统中的集体衰变以及为能量收集和量子传感等应用设计物理系统中的超辐射发射提供了重要的物理见解。