The pump-probe x-ray absorption spectroscopy as an ultrafast thermometer of out of equilibrium systems*

We propose to use pump-probe x-ray absorption spectroscopy (XAS) as an ultrafast thermometer of the electronic subsystem, when it is driven out of equilibrium. The idea is inspired by the fact that the shape of the so-called satellite peak in the x-ray photoemission spectra (XPS) depends strongly on temperature in equilibrium. This satellite peak also demonstrates a strong dependence on time in time-resolved spectroscopy, and it is connected to the total energy of the system. Further, by comparing the energy gain during the nonequilibrium process to the equilibrium energy, allows one to measure in situ the effective temperature of the thermalized electron state. XAS is closely connected to XPS and might be an effective thermometer of the nonequilibrium system and it can be performed in many experiments where ultrafast x-rays are available.
We solve the XAS in the spinless Falicov-Kimball model within the dynamical mean-field theory, which gives an exact result. We examine metallic and Mott-insulator phases of the model.