Ultra-fast inner-shell electron dynamics and electron correlations are fundamental to characterize atomic and molecular states, their structure and dynamics, which are at the heart of chemical reactions and biochemical processes. Nonlinear wave mixing in the X-ray range can provide valuable insights into the structural and electron dynamics of atomic and molecular systems on ultrafast time scales, with state- and site-selectivity and atomic resolution. In particular, resonant X-ray four-wave mixing (XFWM) can deliver information about coherence, complex orbital relaxations and electron dynamics, being locally initiated near a specifi c atom. We will discuss the successful realization of a XFWM process at the Swiss free electron laser (SwissFEL), at which we have measured background-free XFWM signals from Neon with all interacting photons in the X-ray regime [1,2]. This fi rst all-X-ray four-wave-mixing approach represents a major breakthrough towards coherent multidimensional X-ray spectroscopy and the general application of nonlinear X-ray wave-mixing. However, many chemical reactions and almost all biological chemistry occur in liquid solutions necessitating the investigation of solvent and solvation dynamics. To the best of our knowledge, no hard X-ray-FWM experiment has been realized in a liquid sample so far. We will additionally discuss preliminary results from a mixed X-ray/optical FWM measurement in pure water and in Ferrioxalate aquaeous solution in a micro-meter liquid jet [3] and give a perspective to more complex biological systems.

[1]A.S. Morillo-Candas et al., ‘All x-ray four-wave mixing on a gas phase sample’, CLEO/Europe-EQEC/pp1–1,(2023).
[2]A.S. Morillo-Candas et al., Coherent all X-ray four wave mixing at core shell resonances, arXiv:2408.11881[-physics.optics],(2024).(&submitted).
[3]A.S. Morillo-Candas et al., ‘Time resolved hard x-ray/optical transient grating spectroscopy on a liquid jet’, CLEO/Europe-EQEC/pp 1–1,(2023).