Scaling theory of decoherence in Dicke superradiance

The survival of many-body coherence depends on the competition between correlation buildup and decoherence. In Dicke superradiance, collective emission builds up correlations, producing a peak intensity scaling as $N^2$ for $N$ emitters. We develop a scaling theory including local dephasing and spontaneous emission and obtain fully collective, partially collective, and independent-emitter scaling regimes. The boundary of the fully collective regime defines a continuous phase transition in a transient observable. Local decoherence can prevent $N^2$ scaling despite increasing $N$.