  Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable
tool to probe the nature, couplings, and lifetimes of excitations in quantum
materials. It thus promises to identify unique signatures of spin liquid states
in quantum magnets by directly probing properties of their exotic
fractionalized excitations. Here, we calculate the second-order 2DCS of the
Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints
appear already in this lowest-order nonlinear response
$\chi^{(2)}_{yzx}(\omega_1, \omega_2)$ when using crossed light polarizations.
We further relate the off-diagonal 2DCS peaks to the localized nature of the
matter Majorana excitations trapped by $\mathbb{Z}_2$ flux excitations and show
that 2DCS thus directly probes the inverse participation ratio of Majorana
wavefunctions. By providing experimentally observable features of spin liquid
states in the 2D spectrum, our work can guide future 2DCS experiments on Kitaev
magnets.
