Dicke superradiance requires interactions beyond nearest-neighbors

TL;DR

This paper demonstrates that Dicke superradiance requires interactions beyond nearest neighbors, establishing a theoretical bound on emission rates and identifying the minimal interaction range necessary for superradiance.

Contribution

The authors develop a new theoretical method to bound superradiant emission and prove that nearest-neighbor interactions alone cannot produce superradiance in ordered arrays.

Findings

Superradiance requires next-nearest-neighbor interactions.

Bound on emission rate using spectral radius of auxiliary Hamiltonian.

Critical coupling for exponential decay interactions is dimension-independent.

Abstract

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.