Distinguishing Nonlinear Terahertz Excitation Pathways with Two-Dimensional Spectroscopy.

High-field terahertz (THz) spectroscopy is enabling the ultrafast study and control of matter in new and exciting ways. However, when intense electromagnetic pulses are used in any kind of pump-probe spectroscopy, several nonlinear excitation pathways can result, leading to scenarios that required the development of multidimensional spectroscopies to illuminate the observed dynamics. Here we demonstrate a clear example where two-dimensional (2D) THz vibrational spectroscopy is needed to distinguish between nonlinear-excitation pathways in CdWO_{4}. We nonlinearly excite a set of Raman-active vibrational modes in CdWO_{4} with broadband THz pulses, and 2D spectroscopy allows us to determine the dominant excitation pathway. We provide a general framework for 2D THz and multi-THz nonlinear phonon spectroscopy in solid systems, which has important implications in contributing needed clarity to the nascent field of nonlinear phononics.