Theory of Time-Resolved Raman Scattering in Correlated Systems: Ultrafast Engineering of Spin Dynamics and Detection of Thermalization*

Ultrafast characterization and control of elementary excitations are critical to understanding and manipulating emergent phenomena in correlated systems. In particular, spin interaction plays an important role in unconventional superconductivity, but efficient tools for probing spin dynamics especially out of equilibrium is still lacking. Here we develop the theory of time-resolved Raman scattering, which can be a powerful tool for nonequilibrium studies. We also simulate a pumped single-band Hubbard model using exact diagonalization. Different ultrafast processes are shown to exist in the time-resolved Raman spectra and dominate under different pump conditions. For high-frequency and off-resonance pumps, the Floquet theory is shown to work well in capturing the bimagnon softening. We also show that effective heating dominates at small pump fluences, while many-body effect takes over at larger pump amplitudes and frequencies resonant to the Mott gap. Time-resolved Raman scattering thereby provides the platform to explore ultrafast processes and design material properties out of equilibrium.