We investigate time resolved multi-wave mixing in the XUV and X-ray spectral range. From the energy- and q - dependent signals, information about ultrafast charge carrier dynamics and about the subsequent energy dissipation into lattice vibrations and heating is obtained. Using a four wave mixing setup these effects can be distinguished by probing the dynamics at different q vectors and both on and off the specific resonances.
After moving a molecular system out of its equilibrium, e.g. by coupling it to a photon field, the system tends to return to its thermodynamic equilibrium on different time scales, depending on the number of gateway states through which the induced excitation can relax. In relation to the size of the quantum system the induced energy and coherence can relax via intra- and intermolecular ways and as such one may speak of relaxation and transport phenomena. In complex many body quantum systems these effects may not be well separated and collective relaxation can give rise to complex dynamics. Unambiguous association of the time and length scales of collective structural and electronic rearrangements and their control requires direct and simultaneous measurement of both. This can be enabled through coherent nonlinear spectroscopy using X-ray wavelengths. In coherent multiphoton spectroscopies interference occurs when two transitions pathways terminate on the same eigenstate. Time-frequency-resolved multi-wave mixing e.g. allows the preparation, manipulation, and readout of massive quantum superpositions with sufficient control to consider applications towards driving and investigation of the ongoing dynamics.