Classical coherent two-dimensional vibrational spectroscopy

Two-dimensional (2D) ultrafast spectroscopy is a powerful tool for studying the electronic and vibrational structures of complex systems. Unfortunately, the physical interpretation of these experiments is obscured by conceptual problems in classical response theory, i.e., the divergence of classical nonlinear response functions. We demonstrate that these difficulties are avoided by modeling classical 2D experiments nonperturbatively, illustrating that nonlinear spectroscopy and nonlinear response are not synonymous. Numerical simulations allow a direct comparison between classical and quantum 2D spectra for simple, weakly anharmonic systems relevant to vibrational spectroscopy. We find that nonperturbative classical theory-although differing in quantitative details-accurately captures the key qualitative features of the quantum 2D spectrum, including the separation of the signal into wavevector-selected pathways, formation of cross peaks between coupled vibrational modes, and coherent beating in the signal as a function of waiting time (so-called "quantum beats"). These results are discussed in terms of a simple analytical model which captures the key physical features of classical 2D spectroscopy and provides a link between classical and quantum descriptions. One interesting conclusion from this comparison is that the "coherence" observed in ultrafast spectroscopy may (at least in vibrational experiments) be understood as a purely classical phenomenon, without reference to quantum mechanics.