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X-ray free-electron lasers (XFELs) are now able to provide tunable pairs of intense sub-fs pulses in the soft x-ray regime, paving the way for time-resolved investigations of attosecond charge migration in molecules. However, the stochastic shot-to-shot variation of the XFEL pulses may degrade and eventually hide the observable features. We show by means of state-of-the-art calculations that the damping of the charge migration induced by 260 eV pulses in p-aminophenol due to the shot-to-shot variation of pulses generated at the Linac Coherent Light Source is negligible in comparison to the natural damping due to the intrinsic fluctuation of the initial molecular geometry. This result gives us confidence in the utility of XFEL sub-fs pulses for the measurement of charge migration and other ultrafast charge dynamics.

Real-time observations of the coherent electron dynamics induced by ultrashort light pulses in condensed-matter systems have remained elusive due to limitations in existing attosecond devices. Here we show that attosecond transient absorption resulting from an IR-pump/x-ray probe numerical experiment performed in graphene unambiguously encodes the information of the coherent electron dynamics induced by the pump pulse. First, we demonstrate the possibility of tracking in real time the electron injection through the Dirac points. Second, we derive and demonstrate a simple semiclassical theory that correlates the energy structure and the action Berry phase with strong changes in the absorption spectrum around Van Hove singularities. Our work opens the way to the development of novel imaging techniques in condensed matter systems at the attosecond timescale.