  We show that the new technique of terahertz 2D coherent spectroscopy is
capable of giving qualitatively new information about fractionalized spin
systems. For the prototypical example of the transverse field Ising chain, we
demonstrate theoretically that, despite the broad continuum of excitations in
linear response, the 2D spectrum contains sharp features that are a coherent
signature of a `spinon echo', which gives previously inaccessible information
such as the lifetime of the two-spinon excited state. The effects of disorder
and finite lifetime, which are practically indistinguishable in the linear
optical or neutron response, manifest in dramatically different fashion in the
2D spectra. Our results may be directly applicable to model quasi-1D transverse
field Ising chain systems such as CoNb$_2$O$_6$, but the concept can be applied
to fractionalized spin systems in general.
