Recent pump-probe experiments have uncovered a variety of intriguing dynamics in strongly correlated materials such as ultrafast structural transitions in transition metal dichalcogenides. The key feature of these experiments is the time-dependent spectroscopic information. In this talk, I will discuss the time-evolution of various spectroscopic observables in optically excited Mott-Hubbard models. By numerically exact simulations of finite Hubbard clusters, we find that continuous resonant excitation can lead to a prethermal Floquet state with Rabi oscillations for weak field amplitudes . For strong and short excitation, multi-photon excited states show second harmonic oscillations in time-dependent optical conductivity .
 J. Okamoto, F. Peronaci, arXiv:2010.00326.
 J. Okamoto, New J. Phys. 21, 123040 (2019).