  We study theoretically the nonlinear optical response of Tomonaga-Luttinger
spin liquid in the context of terahertz (THz) two-dimensional coherent
spectroscopy (2DCS). Using the gapless phase of the XXZ-type spin chain as an
example, we show that its third-order nonlinear magnetic susceptibilities
$\chi^{(3)}_{+--+}$ and $\chi^{(3)}_{-++-}$ exhibit photon echo, where $\pm$
refers to the left/right-hand circular polarization with respect to the $S^z$
axis. The photon echo arises from a ``lensing'' phenomenon in which the wave
packets of fractional excitations move apart and then come back toward each
other, amounting to a refocusing of the excitations' world lines.
Renormalization group irrelevant corrections to the fixed point Hamiltonian
result in dispersion and/or damping of the wave packets, which can be
sensitively detected by lensing and consequently the photon echo. Our results
thus unveil the strength of THz-2DCS in probing the dynamical properties of the
collective excitations in a prototypical gapless many-body system.
