Theory of time-resolved optical spectroscopy on correlated electron systems

The real-time dynamics of interacting electrons out of equilibrium contains detailed microscopic information about electronically correlated materials, which can be read out with time-resolved optical spectroscopy. The reflectivity that is typically measured in pump-probe experiments is related to the nonequilibrium optical conductivity. We show how to express this quantity in terms of real-time Green's functions using dynamical mean-field theory. As an application we study the electrical response of the Falicov-Kimball model during the ultrafast buildup of the gapped phase at large interaction.