Diffractive optics-based six-wave mixing: Heterodyne detection of the full $χ(5)$ tensor of liquid $CS2$

This work exploits the passive phase stabilization of diffractive optics to implement heterodyne detection of the complete $χ(5)$ tensor of liquid $CS2$ as an example of a simple liquid. This approach permits the use of two different colors for the excitation, probe, and detection beam protocols and enables full optimization of the signal with respect to discrimination against lower order cascaded third-order responses. This work extends the previous study of polarization selectivity, in combination with heterodyne detection, to all independent polarization components to provide further insight into the origins of the fifth-order response and its connection to the multitime correlation of the liquid dynamics. The characteristic feature that clearly distinguishes the direct fifth-order response from lower order cascades is the pronounced ridge along the $τ4$ axis (probe pulse delay) with very rapid decay along the $τ2$ axis (excitation pulse delay). This observation is in contrast to recent related work using one-color homodyne detection. With the determination of the direct fifth-order and cascaded third-order signal amplitudes made possible by heterodyne detection, this difference can be attributed to cross terms between the direct fifth-order and cascaded third-order terms inherent to homodyne detection under phase matching conditions used to discriminate against cascades. In support of theoretical treatments, the previously predicted enhancement of rephasing pathways for certain polarization components has been observed. However, even for these tensor elements the remarkable feature is the very rapid decay in the nuclear coherence along $τ2.$ The experiment is predicated on the ability of a 2-quantum transition involving the Raman overtone to rephase the nuclear coherence. These findings indicate that the nuclear motions, in the frequency range accessed, are strongly damped and draw into question the validity of the overtone as a viable pathway for rephasing. With the isolation of the direct fifth-order Raman response, new information regarding relaxation and dephasing pathways in liquids can be determined for the highest frequency modes. The results are in very good agreement with a recent finite field molecular dynamics simulation of liquid $CS2$ with respect to the polarization dependence of signal magnitudes, relative cascade signal amplitudes, and qualitative agreement with respect to the predicted temporal profiles.