Ultrafast spectroscopy is dominated by time domain methods such as pump-probe and, more recently, 2D-IR spectroscopies. In this paper, we demonstrate that a mixed frequency/time domain ultrafast four wave mixing (FWM) approach not only provides similar capabilities, but it also provides optical analogues of multiple- and zero-quantum heteronuclear nuclear magnetic resonance (NMR). The method requires phase coherence between the excitation pulses only over the dephasing time of the coherences. It uses twelve coherence pathways that include four with populations, four with zero-quantum coherences, and four with double-quantum coherences. Each pathway provides different capabilities. The population pathways correspond to those of two-dimensional (2D) time domain spectroscopies, while the double- and zero-quantum coherence pathways access the coherent dynamics of coupled quantum states. The three spectral and two temporal dimensions enable the isolation and characterization of the spectral correlations between different vibrational and/or electronic states, coherence and population relaxation rates, and coupling strengths. Quantum-level interference between the direct and free-induction decay components gives a spectral resolution that exceeds that of the excitation pulses. Appropriate parameter choices allow isolation of individual coherence pathways. The mixed frequency/time domain approach allows one to access any set of quantum states with coherent multidimensional spectroscopy.

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We report a two-color frequency domain triply vibrationally enhanced (TRIVE) four-wave mixing (FWM) method that is fully resonant and provides coherent multidimensional vibrational spectra. Temporal and spectral discrimination allow control of the coherent interference of multiple pathways including isolation of a specific pathway and coherent control of the relative intensities of peaks in a 2D spectrum. The method is the coherent analogue to two-color pump−probe spectroscopy and allows the dissection of the individual pathways.

The line shapes and intensities in coherent multidimensional vibrational spectra are determined by amplitude level interference between different nonlinear processes. The relative amplitude and phase of each process is controlled by the transition moments and dephasing rates associated with each coherence in a nonlinear pathway. The important nonlinear pathways involve processes that are doubly vibrationally enhanced (DOVE) and nonresonant. The DOVE processes are sensitive to dephasing-induced resonances that change the appearance of two-dimensional spectral features. To understand how these contributions interfere to create a twodimensional vibrational spectrum, line shapes were measured in the frequency domain for a set of model compounds over a range of vibrational frequencies. The amplitudes and dephasing rates for each pathway were determined by modeling spectra. By comparing the amplitudes with a deuteriobenzene internal standard, quantitative values were obtained for the DOVE processes. The results agree with recent ab initio calculations of the third-order DOVE susceptibilities, previous measurements of the concentration dependence, and estimates based on the absorption and Raman cross-sections of each resonance. The interference effects make the DOVE measurements sensitive to the sign of the transition moments.