Free electron lasers (FELs) generate high intensity, ultrafast and coherent X-Ray pulses that are tunable to the elemental edges of interest. We develop and use nonlinear X-Ray techniques at FELs to investigate ultrafast dynamics in solids. Specifically, X-Ray Second Harmonic Generation (XUV-SHG) has been our main spectroscopic tool. In principle, XUV-SHG is particularly attractive as it unites the core-level specificity of X-Ray spectroscopies with the unique properties of second harmonic generation (SHG). As second-order nonlinear process, the SHG is only permitted in media without inversion symmetry. This makes SHG sensitive specific to surfaces and interfaces in cases when the bulk of the material is version symmetric. In combination with X-rays, that have a high penetration depth, this is especially useful to study the electronic sturcture of buried interfaces as seen from one atomic species of the lattice. In addition, SHG can be used to study symmetry-broken media, where then SHG stems from the bulk. In this case, the atomic specificity of X-rays enable to study how a certain atomic species in a lattice contributes to a symmetry-broken state. The XUV-SHG spectra obtained are spectra of the second-order nonlinear susceptibility, which is ultimately a second-rank tensor, i.e., containing also directional information of the dielectric environment.
In our recent experiments, we have studied bulk non-centrosymmetric crystals using XUV-SHG [1,2]. In these crystals due to ion displacements in the unit cell, emergent order such as ferroelectricity appears which makes them an ideal candidate for XUV-SHG studies. In the case of the polar ferroelectric LiOsO3, we demonstrated that the polar phase establishes as a result of Li ion displacements, while by investigating the polarization of XUV-SHG emitted from a well-studied ferroelectric, LiNbO3, we established that the long-accepted theories of angular anisotropy in optical SHG is applicable to XUV-SHG. Along with these studies, we also contributed to the investigation of tabletop sources that achieve XUV-SHG  and demonstrated the capability of XUV-SHG to investigate challenging buried interfaces .
In future experiments we plan to expand XUV-SHG to conduct time-resolved measurements investigating symmetry changes of materials in real-time. We are also exploring the possibility to conduct soft X-ray SHG on liquid jets to learn more about molecular level interactions at the interface of liquids.
 E. Berger, S. Jamnuch, C. Uzundal, C. Woodahl, H. Padmanabhan, P. Manset, Y. Hirata,I. Matsuda, V. Goplan, Y. Kubota,et al., “Extreme Ultraviolet Second Harmonic Generation Spectroscopy in a Polar Metal”, Nano Letters, advanced online publication, (2021)- doi: https://doi.org/10.1021/acs.nanolett.1c01502
 C. B. Uzundal, S. Jamnuch, E. Berger, C. Woodahl, P. Manset, Y. Hirata, T. Sumi, A. Amado, H. Akai, Y. Kubota, et al., “Polarization-Resolved Extreme Ultraviolet Second Harmonic Generation from LiNbO3” (2021), arXiv:2104.01313
 T. Helk, E. Berger, S. Jamnuch, L. Hoffmann, A. Kabacinski, J. Gautier, F. Tissandier, J. P. Goddet, H.-T. Chang, J. Oh, C. D. Pemmaraju, T. A. Pascal, S. Sebban, C. Spielmann, M. Zuerch. “Table-top extreme ultraviolet second harmonic generation”, Science Advances 7, eabe2265 (2021)
 C. P. Schwartz, S. L. Raj, S. Jamnuch, C. J. Hull, P. Miotti, K. Lam, D. Nordlund, C. B.Uzundal, C. D. Pemmaraju, L. Foglia,et al., “Angstrom-resolved Interfacial Structure in Organic-Inorganic Junctions,” (2020), arXiv:2005.01905, in press PRL