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Two dimensional coherent spectroscopy (2DCS) probes the nonlinear opticalresponse of correlated systems. An interesting application is the study offractionalized excitations, which are challenging to distinguish unambiguouslyin linear response. Here we demonstrate how the sensitivity of optical matrixelements to variations in the photon polarization allows one to probe differentaspects of low lying excitations in models of the candidate fractionalizedmaterials Ce$_2$Zr$_2$O$_7$ and Nd$_2$Zr$_2$O$_7$, which host effectiveone-dimensional spin chains when subjected to a [110] magnetic field. We showhow both fractionalized spinon excitations or conventional magnons can bepicked out in the 2DCS response, and how the response from polarized spinchains can be used to probe the dipolar-octupolar mixing angle $\theta$ throughthe relative intensity of one- and two-magnon signals. Further, we find that a$[001]$ polarization of the probe field is particularly sensitive to lower bandedge of the spinon continuum and can be used as a measure of the proximity of aquantum critical point in Ce$_2$Zr$_2$O$_7$. 2DCS can thus be employed toprovide invaluable and detailed information both on the constituent degrees offreedom of a quantum material and on their collective behaviour.

Exploiting polarization dependence in two dimensional coherent spectroscopy: examples of Ce$_2$Zr$_2$O$_7$ and Nd$_2$Zr$_2$O$_7$