Single- and double-quantum nonlinear spectroscopy of anharmonic vibrational polaritons

We have recently introduced a theoretical framework for describing the ultrafast nonlinear optical response of molecular polaritons—hybrid light–matter states formed by ensembles of $N$ molecules strongly coupled to a cavity photon mode. Our approach combines a semiclassical mean-field description of the coupled molecular and cavity dynamics with a perturbative expansion in the external driving fields and can be viewed as a generalization of conventional free-space spectroscopy. By further expanding in the pulse phases, distinct excitation pathways in Liouville space and their respective contributions to the nonlinear signal can be resolved. We highlight applications in pump–probe spectroscopy of polariton transport and compute 2D single- and double-quantum coherence spectra, discussing the role of vibrational anharmonicity on the resulting spectra and comparing with recent experiments. Finally, we show that the perturbative nonlinear polariton spectroscopy framework can be readily integrated with finite-difference time-domain (FDTD) simulations, enabling the description of nonlinear spectroscopy in arbitrary electromagnetic environments.