Theory of Time-Resolved Responses in Transient Floquet Systems

Time-resolved spectroscopy has emerged as a powerful technique to investigate far-from-equilibrium physics. Motivated by pump-probe experiments, we develop a formalism to calculate the time-resolved response of a material quenched by Floquet driving with light or a phonon mode and then probed by an ultrafast pulse. In contrast to previous studies, we do not assume the system has reached a steady state when the probe starts, allowing us to track the spectroscopic response as the system prethermalizes. We find that the response can have spectral peaks which do not correspond to the probe frequency nor the harmonics of the drive and which depend on the time of the probe pulse. These findings are illustrated in the optical response of a transition metal oxide driven by a phonon mode. We also discuss the selection rules originating from dynamical symmetries in optical responses for non-steady state systems.