Absence of entanglement growth in Dicke superradiance

Dicke superradiance describes an ensemble of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>N</a:mi> </a:math> permutationally invariant two-level systems collectively emitting radiation with a peak radiated intensity scaling as <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msup> <b:mi>N</b:mi> <b:mn>2</b:mn> </b:msup> </b:math> . Individual Dicke states are typically entangled. However, the density matrix during superradiant decay is a mixture of such states, raising the subtle question of whether the total state is entangled or separable. We resolve this by showing analytically that for any <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>N</c:mi> </c:math> , starting from the fully excited state, the collective decay preserves separability for all times. This answers a longstanding question on the role of entanglement in Dicke superradiance and underscores that, despite collective dissipation, separable states remain separable under these dynamics.