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Ultrafast characterization and control of many-body interactions andelementary excitations are critical to understanding and manipulating emergentphenomena in strongly correlated systems. In particular, spin interaction playsan important role in unconventional superconductivity, but efficient tools forprobing spin dynamics especially out of equilibrium, are still lacking. Toaddress this question, we develop a theory for nonresonant time-resolved Ramanscattering, which can be a generic and powerful tool for nonequilibriumstudies. We also use exact diagonalization to simulate the pump-probe dynamicsof correlated electrons in the square-lattice single-band Hubbard model.Different ultrafast processes are shown to exist in the time-resolved Ramanspectra and dominate under different pump conditions. For high-frequency andoff-resonance pumps, we show that the Floquet theory works well in capturingthe softening of bimagnon excitation. By comparing the Stokes/anti-Stokesspectra, we also show that effective heating dominates at small pump fluences,while a coherent many-body effect starts to take over at larger pump amplitudesand frequencies on resonance to the Mott gap. Time-resolved Raman scatteringthereby provides the platform to explore different ultrafast processes anddesign material properties out of equilibrium.

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