Authors
Cosimo C Rusconi, Eric Sierra, Wai-Keong Mok, Avishi Poddar, Simon B Jäger, Ana Asenjo-Garcia
Published in
Physical review letters. Volume 137. Issue 14. Pages 143603. Oct 02, 2026.
Abstract
Cooperative emission is well understood for idealized symmetric systems, but its fundamental limits in spatially extended, free-space ensembles remain an open question. Here, we derive a universal law for the scaling of the maximum photon emission rate with system size that unifies both ordered arrays and disordered atomic clouds in arbitrary dimensions at fixed density. We demonstrate that, for a fixed atomic density, the maximum emission rate scales universally as the product of the atom number and the system's geometric optical depth. The geometric optical depth differs from the result of the Beer-Lambert law at high density and encodes the dimensional scaling across all regimes from independent emission to the Dicke limit. Furthermore, we establish a scaling law for directional detection, revealing that the observed rate depends on the detector's numerical aperture: small apertures yield Dicke-like quadratic scaling, whereas large apertures recover our integrated universal bound. Our results establish optical depth as the parameter governing many-body cooperative emission in both ordered and disordered ensembles, and reveal that directional and total-emission scalings must be carefully distinguished in experimental settings.
PMID:
42886916
Bibliographic data and abstract were imported from PubMed on 17 Oct 2026.
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