The optical response of matter to light electric fields is intimately connected to the electronic structure and dynamics of the target under study. In the linear regime, the interaction is well understood through Maxwell’s classical description of light waves, and the response of the system is captured in the medium’s refractive index, encoding both absorption and dispersion. Absorbing XUV and x-ray light, atom-specific inner-shell and core-shell transitions can be resonantly excited, providing a characteristic spectroscopic fingerprint of each system. Given the availability of free-electron lasers (FELs), delivering intense XUV and x-ray pulses at the femtosecond and attosecond timescale, new opportunities open up for the exploration of the nonlinear regime, with the ultimate goal to selectively steer the ultrafast quantum dynamics of matter at the fundamental electronic level inside atoms and molecules. In this talk I will give an overview of our activities in the development of new concepts for nonlinear XUV-optical absorption spectroscopy with FEL light sources. We have developed a versatile beamline for XUV-pump–XUV-probe transient absorption spectroscopy that was operated at the open-port beamline BL2 at the free-electron laser in Hamburg (FLASH) . This has enabled the observation of XUV-intensity-induced modifications of the FEL absorption in atoms [2-7] which can be related to nonlinear interactions, including strong-coupling effects of resonant transitions. Last but not least, by identifying individual resonances in different molecular-fragment species, this technique also creates new opportunities for tracking site-specific molecular dynamics at an ultrafast timescale [8,9].
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