Nonlinear spectroscopy of resonantly coupled classical mechanical molecular vibrations

The signal in a coherent, nonlinear vibrational spectroscopy measurement such as the vibrational echo, the analog in vibrational spectroscopy of the spin echo of magnetic resonance, may be computed from a third-order nonlinear response function. The challenges of the quantum mechanical calculation of this response function for many coupled anharmonic degrees of freedom motivate the analysis of the response function in classical mechanics. We compare calculations of the classical third-order nonlinear response function for two models of resonantly coupled anharmonic oscillators. Our analysis elucidates the effects on nonlinear molecular vibrational spectroscopy of resonant coupling among molecular vibrations and of anharmonicity, and provides connections between quantum and classical pictures of nonlinear spectroscopic processes.