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

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 +/- 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.

Automated summary

The theoretical study investigates the nonlinear optical response of Tomonaga-Luttinger spin liquids in the context of terahertz two-dimensional coherent spectroscopy. Specifically, the third-order nonlinear magnetic susceptibilities of the XXZ-type spin chain exhibit photon echo, demonstrating the potential of THz 2DCS in probing the dynamical properties of collective excitations in gapless many-body systems. Renormalization-group-irrelevant corrections to the fixed-point Hamiltonian result in dispersion and/or damping of wave packets, which can be sensitively detected by lensing and the photon echo phenomenon.