Resonant nonlinear X-ray spectroscopy of acetyl fluoride for probing electronic dynamics with space selectivity

Ultrashort, coherent X-ray pulses from X-ray free-electron lasers (FELs) enable direct access to core excited states in ultrafast time scales. They can be used to extend multidimensional nonlinear spectroscopy into the X-ray regime, and probe the dynamics of a large number of valence and core excited states thanks to their broad bandwidths. Here, we present resonant X-ray sum-frequency-generation (XSFG) signals in order to access novel information on molecular dynamics. In XSFG, the dynamics of a valence electronic wave packet, initiated by an optical or ultraviolet pulse, are subsequently probed by a coherent resonant X-ray pulse with a properly set delay. By resonantly exciting different element-specific core states, the X-ray probe can be employed to monitor the molecular dynamics with high spatial selectivity. Due to their short wavelengths, hard-X-ray FEL pulses are also sensitive to spatial variations within the size of the molecule. Using the minimal-coupling Hamiltonian, we show how XSFG can reveal effects going beyond a description of the light-matter interaction based on the multipole expansion.