  Cooperative effects of multiple quantum emitters are characterized by
transitions via delocalized collective states with altered emission properties
due to the existence of inter-emitter coherences. When realized with excitonic
condensed matter nanostructures, these effects are significantly affected by
the presence of strong emitter-phonon coupling, which leads to the formation of
polarons. We show that, while for single-emitter emission into free space this
formation has no impact on its radiative lifetime, the same is not true for
superradiant emission. Considering the case of two indistinguishable quantum
emitters, we analyse how polaron dressing affects collective photon emission by
mixing bright and dark Dicke states. Our numerical simulations show that this
mixing crucially depends on the circumstances of the excitation of the system:
Depending on the pulse length of an exciting laser, one can choose to either
prepare polaronic Dicke states, or bare electronic Dicke states, changing the
superradiant decay characteristics of the system. Additionally, we derive
analytic expressions for these limiting cases, which match the results of
numerically exact calculations.
