Detecting electronic coherence by multidimensional broadband stimulated x-ray Raman signals

Nonstationary molecular states which contain electronic coherences can be impulsively created and manipulated by using recently developed ultrashort optical and x-ray pulses via photoexcitation, photoionization, and Auger processes. We propose several stimulated-Raman detection schemes that can monitor the subsequent phase-sensitive electronic and nuclear dynamics. Three detection protocols of an x-ray broadband probe are compared: frequency-dispersed transmission, integrated photon number change, and total pulse energy change. In addition, each can be either linear or quadratic in the x-ray probe intensity. These various signals offer different gating windows into the molecular response, which is described by correlation functions of electronic polarizabilities. Off-resonant and resonant signals are compared.