Photon Echo from Lensing of Fractional Excitations in Tomonaga-Luttinger Spin Liquid

Abstract

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 χ_{+--+}^{(3)} and χ_{-++-}^{(3)} exhibit photon echo, where ± refers to the left- or 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.