Ultrafast thermometry of nonequilibrium electrons via the X-ray core-hole photoelectron and X-ray absorption spectroscopies*

Pump-probe spectroscopy is extensively applied to study ultrafast relaxation processes in the electron systems out of equilibrium. But we still lack an ultrafast means to perform thermometry. From our previous work on the time-resolved X-ray photoemission spectroscopy (tr-XPS), we found a strong correlation between the integrated weights of the peaks on the spectra, with the thermal occupancies of the appropriate many-body states. This approach can serve as a probe of the energy (and therefore the effective temperature) of the excited electrons. The advantage of X-ray absorption spectroscopy (XAS) is that it is photon-in-photon-out experiment, which is easier to set up. XPS and XAS spectroscopies are closely connected, so we expect there is a similar correlation between the peaks of a tr-XAS spectra and the energy of the excited electrons that can be exploited as another effective thermometer of the nonequilibrium state. We illustrate how this works in the metallic and Mott-insulator phases of the spinless Falicov-Kimball model within nonequilibrium dynamical mean-field theory.