Four-wave mixing experiments with extreme ultraviolet transient gratings

Four-wave mixing (FWM) processes, based on third-order nonlinear light-matter interactions, can combine ultrafast time resolution with energy and wavevector selectivity, and enable the exploration of dynamics inaccessible by linear methods(1-7). The coherent and multi-wave nature of the FWM approach has been crucial in the development of advanced technologies, such as silicon photonice, subwavelength imaging' and quantum communications(10). All these technologies operate at optical wavelengths, which limits the spatial resolution and does not allow the probing of excitations with energy in the electronvolt range. Extension to shorter wavelengths that is, the extreme ultraviolet and soft-X-ray ranges would allow the spatial resolution to be improved and the excitation energy range to be expanded, as well as enabling elemental selectivity to be achieved by exploiting core resonances(5-7,11-14). So far, FWM applications at such wavelengths have been prevented by the absence of coherent sources of sufficient brightness and of suitable experimental set-ups. Here we show how transient gratings, generated by the interference of coherent extreme-ultraviolet pulses delivered by the FERMI free-electron laser(15), can be used to stimulate FWM processes at suboptical wavelengths. Furthermore, we have demonstrated the possibility of observing the time evolution of the FWM signal, which shows the dynamics of coherent excitations as molecular vibrations. This result opens the way to FWM with nanometre spatial resolution and elemental selectivity, which, for example, would enable the investigation of charge-transfer dynamics(5-7). The theoretical possibility of realizing these applications has already stimulated ongoing developments of free-electron lasers(16-20): our results show that FWM at suboptical wavelengths is feasible, and we hope that they will enable advances in present and future photon sources.