Four wave mixing experiments with extreme ultraviolet transient gratings

Four wave mixing (FWM) processes, based on third-order non-linear light-matter interactions, can combine ultrafast time resolution with energy and wavevector selectivity, and enables to explore dynamics inaccessible by linear methods.(1-7) The coherent and multi-wave nature of FWM approach has been crucial in the development of cutting edge technologies, such as silicon photonics,(8) sub-wavelength imaging(9) and quantum communications.(10) All these technologies operate with optical wavelengths, which limit the spatial resolution and do not allow probing excitations with energy in the eV range. The extension to shorter wavelengths, that is the extreme ultraviolet (EUV) and soft-x-ray (SXR) range, will allow to improve the spatial resolution and to expand the excitation energy range, as well as to achieve elemental selectivity by exploiting core resonances.(5-7,11-14) So far FWM applications at these wavelengths have been prevented by the absence of coherent sources of sufficient brightness and suitable experimental setups. Our results show how transient gratings, generated by the interference of coherent EUV pulses delivered by the FERMI free electron laser (FEL),(15) can be used to stimulate FWM processes at sub-optical wavelengths. Furthermore, we have demonstrated the possibility to read the time evolution of the FWM signal, which embodies the dynamics of coherent excitations as molecular vibrations. This result opens the perspective for FWM with nanometer spatial resolution and elemental selectivity, which, for example, would enable the investigation of charge-transfer dynamics.(5-7) The theoretical possibility to realize these applications have already stimulated dedicated and ongoing FEL developments;(16-20) today our results show that FWM at sub-optical wavelengths is feasible and would be the spark to the further advancements of the present and new sources.