Out of equilibrium thermometry with pump-probe x-ray photoemission spectroscopy

We calculate the spectral function of a deep core-level hole in a pump-probe x-ray photoemission spectroscopy experiment. Here, an intense light pulse pumps electrons to higher energies, and a second high-energy x-ray probe pulse is used to knock out an electron from a deep core-level. Electrons from the conduction band feel the effects of the core-hole potential and react by screening it. This creates particle-hole excitations within the conduction band until the core-hole has been filled. We examine the spinless Falicov-Kimball model, which possesses a metal-Mott-insulator transition, and has an exact solution within dynamical mean-field theory. In linear response, it is well known that the shape of the core-hole spectra depends strongly on temperature in the high-temperature regime. We employ this effect in nonequilibrium, and describe an ultrafast "thermometer," which can determine the energy content of the conduction electrons with a nondestructive in situ measurement on an ultrafast time scale.