Molecular polaritons have gained considerable attention due to their potential to control nanoscale molecular processes by harnessing electromagnetic coherence. Although recent experiments with liquid-phase vibrational polaritons have shown great promise for exploiting these effects, significant challenges remain in interpreting their spectroscopic signatures. We develop a quantum-mechanical theory of pump-probe spectroscopy for this class of polaritons based on the quantum Langevin equation and the input-output theory. Comparison with recent experimental data shows good agreement upon consideration of the various vibrational anharmonicities that modulate the signals. Finally, a simple and intuitive interpretation of the data based on an effective mode-coupling theory is provided. Our work provides a solid theoretical framework to elucidate nonlinear optical properties of molecular polaritons as well as to analyze further multidimensional spectroscopy experiments on these systems.

We report the first experimental two-dimensional infrared (2D IR) spectra of novel molecular photonic excitations - vibrational-polaritons. The application of advanced 2D IR spectroscopy onto novel vibrational-polariton challenges and advances our understanding in both fields. From spectroscopy aspect, 2D IR spectra of polaritons differ drastically from free uncoupled molecules; from vibrational-polariton aspects, 2D IR uniquely resolves hybrid light-matter polariton excitations and unexpected dark states in a state-selective manner and revealed hidden interactions between them. Moreover, 2D IR signals highlight the role of vibrational anharmonicities in generating non-linear signals. To further advance our knowledge on 2D IR of vibrational polaritons, we develop a new quantum-mechanical model incorporating the effects of both nuclear and electrical anharmonicities on vibrational-polaritons and their 2D IR signals. This work reveals polariton physics that is difficult or impossible to probe with traditional linear spectroscopy and lays the foundation for investigating new non-linear optics and chemistry of molecular vibrational-polaritons.

We report experimental 2D infrared (2D IR) spectra of coherent light-matter excitations--molecular vibrational polaritons. The application of advanced 2D IR spectroscopy to vibrational polaritons challenges and advances our understanding in both fields. First, the 2D IR spectra of polaritons differ drastically from free uncoupled excitations and a new interpretation is needed. Second, 2D IR uniquely resolves excitation of hybrid light-matter polaritons and unexpected dark states in a state-selective manner, revealing otherwise hidden interactions between them. Moreover, 2D IR signals highlight the impact of molecular anharmonicities which are applicable to virtually all molecular systems. A quantum-mechanical model is developed which incorporates both nuclear and electrical anharmonicities and provides the basis for interpreting this class of 2D IR spectra. This work lays the foundation for investigating phenomena of nonlinear photonics and chemistry of molecular vibrational polaritons which cannot be probed with traditional linear spectroscopy.