Disorder-induced dark states line shape in pump-probe spectroscopy of polaritons

The formation of hybrid light-matter states called polaritons provides a route to shape the photophysics and photochemistry of molecules. Accordingly, the dynamics of polaritons following photoexcitation is extensively studied. In particular, the role of the dark state manifold in such processes remains unclear. Here, we investigate the line shape of pump-probe spectra of polaritons emerging at the dark states energy under the influence of disorder. Previously, we already investigated the pump-probe line shapes of polaritons in a disorder-free model and identified distinct signatures of relaxation into dark states, thus providing an indirect probe of this relaxation. Since the transition dipole moment of dark states vanishes in a disorder-free model, they cannot be directly probed. However, dark states acquire small transition dipole moments as soon as disorder is explicitly included in the model, enabling them to be directly probed. In this work, we demonstrate that the inclusion of the relaxation to dark states and disorder leads to the evolution of the spectral shape at the dark states energy from a derivative-like into an absorptive line shape. Furthermore, we investigate the dependence of the line shape on the disorder strength and its asymptotic scaling for a large number of coupled molecules. Our results demonstrate that probing dark states can help to single out the polaritonic response from the total signal.