Probing the anharmonicity of vibrational polaritons with double-quantum two-dimensional infrared spectroscopy.

Strong coupling between the molecular vibrations and electromagnetic fields of light confined to an infrared cavity leads to the formation of vibro-polaritons - quasi-particles thought to provide the means to control the rates of chemical reactions inside a dark cavity. Despite the mechanisms indicating how vibrational coupling to the vacuum fields can affect the reaction rates are still not well understood, it has been recently demonstrated that the formation of the polariton states alters the ultrafast relaxation dynamics of the strongly coupled system. The relaxation dynamics in molecules, which is known to be important for the chemical reactivity, is directed by anharmonic couplings involving multiple intra- and inter-molecular vibrational degrees of freedom. However, the impact of the molecular anharmonicity on the polariton states remains elusive. Some theoretical models, employed to interpret the experimental observations, assume that vibrational polaritons are harmonic. Others assume a certain anharmonicity of vibro-polaritons; however, to date, it has not been experimentally determined. Herein, we performed double-quantum two-dimensional third-order nonlinear infrared spectroscopy of the carbonyl stretching (C=O) vibrational modes in a thin film of polymethyl methacrylate polymer (PMMA) strongly coupled to the surface lattice resonances of the periodic arrays of half-wavelength infrared disk antennas. We found that, indeed, the mechanical anharmonicity of polaritons is very small. Quantitatively, our results place an upper bound on a polariton mechanical anharmonicity of 2 cm, compared with that of the C=O mode in a PMMA film of 15 cm. Thus, our results support previous assumptions regarding the harmonic character of vibro-polaritons.