Polarization-sensitive IR-pump-x-ray-probe spectroscopy

X-ray absorption and core-ionization spectra of molecules pumped by two coherent infrared pulses with different polarizations are studied theoretically. We have found a sensitivity of the vibrational profile of x-ray probe spectra to polarizations of the IR and x-ray pulses. This polarization dependence is qualitatively different for x-ray absorption and x-ray photoelectron spectra. Measurements of this polarization dependence allow to select the difference in Franck-Condon distributions from the lowest and pumped vibrational levels of the electronic ground state. The proposed technique is exemplified numerically using x-ray absorption spectra of the pumped CO molecule. We also show that this kind of pump-probe spectroscopy can enable studies of the dynamics of molecular rotation.