  We compute numerically the second and third order nonlinear magnetic
susceptibilities of an Ising ladder model in the context of two-dimensional
coherent spectroscopy by using the infinite time-evolving block decimation
method. The Ising ladder model couples a quantum Ising chain to a bath of
polarized spins, thereby effecting the decay of spinon excitations. We show
that its third order susceptibility contains a robust spinon echo signal in the
weak coupling regime, which appears in the two-dimensional coherent spectrum as
a highly anisotropic peak in the frequency plane. The spinon echo peak reveals
the dynamical properties of the spinons. In particular, the spectral peak
corresponding to the high energy spinons, which couple to the bath, is
suppressed with increasing coupling, whereas those do not show no significant
changes.
