Nonlinear semiclassical spectroscopy of ultrafast molecular polariton dynamics

We introduce a theoretical framework that allows for the systematic and efficient description of the ultrafast nonlinear response of molecular polaritons, i.e., hybrid light-matter states, in particular in the limit of large numbers of molecules $\mathcal N$ coupled to the cavity mode. Our approach is based on a semiclassical, mean-field evolution of the molecular Hamiltonian and the cavity field, complemented by a perturbative expansion of both light and matter counterparts in the input pulses entering the cavity. This formalism can be regarded as an extension of traditional free-space nonlinear spectroscopy, now incorporating the feedback of matter onto the light field via the induced polarization. We demonstrate the utility of the framework by applying it to the calculation of the pump-probe polariton response and in multidimensional coherent polariton spectroscopy.