The development of inelastic x-ray scattering with millielectron volt energy resolution at the European Synchrotron Radiation Facility in Grenoble, France, provides a method for studying high-frequency collective dynamics in disordered systems. This has led to the observation of propagating acoustic phonon-like excitations in glasses and glass-forming liquids down to wavelengths comparable to the interparticle distance. Using the inelastic x-ray scattering results on glycerol as a representative example, it is shown that the microscopic dynamic properties are related to the excess of vibrational states in glasses and to the consequences at the microscopic level of the liquid-glass transition. Moreover, they allow derivation of the infinite frequency sound velocity, a quantity related to the structural relaxation times and to the change of ergodicity at the liquid-glass transition.

Four-wave mixing processes are achieved at suboptical wavelengths by using a free-electron laser as a source to generate extreme ultraviolet pulses that produce transient gratings. The phenomenon of four-wave mixing (FWM) occurs when two wavelengths of light interact to produce two extra wavelengths in the signal. It has been exploited in many optics technologies, from optical fibre communication to spectroscopy. Until now FWM has been limited to optical wavelengths. Here Filippo Bencivenga et al. show how to stimulate four-wave mixing processes at suboptical wavelengths using the FERMI free-electron laser as a source to generate extreme ultraviolet pulses that produce transient gratings. The extension of FWM to shorter wavelengths — combined with new developments in free-electron lasers — promises higher resolution for many techniques and the possibility of probe excitations to higher energies. 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 methods1,2,3,4,5,6,7. The coherent and multi-wave nature of the FWM approach has been crucial in the development of advanced technologies, such as silicon photonics8, subwavelength imaging9 and quantum communications10. 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 resonances5,6,7,11,12,13,14. 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 laser15, 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 dynamics5,6,7. The theoretical possibility of realizing these applications has already stimulated ongoing developments of free-electron lasers16,17,18,19,20: our results show that FWM at suboptical wavelengths is feasible, and we hope that they will enable advances in present and future photon sources.

A propagating excitation with a velocity of sound of $3200\pm 100$ $\mathrm{m}/\mathrm{s}$ is measured in ${\mathrm{H}}_2\mathrm{O}$ at 294 $\mathrm{K}$ between 4 and 14 ${\mathrm{nm}}^{-1\mathrm{}}$, using inelastic x-ray scattering with 5 $\mathrm{meV}$ energy resolution. The existence of fast sound is therefore demonstrated in an energy-momentum region much wider than that of previous neutron measurements on ${\mathrm{D}}_2\mathrm{O}$. The equivalence of the fast sound velocity in ${\mathrm{H}}_2\mathrm{O}$ and in ${\mathrm{D}}_2\mathrm{O}$ rules out models where this mode propagates only on the hydrogen network. These results show the ability of inelastic x-ray scattering to study the collective dynamics of liquids.

High energy resolution inelastic x-ray scattering measurements in the $1–6{\mathrm{nm}}^{-1\mathrm{}}$ momentum transfer ( $Q$) region in vitreous silica ( $v{-\mathrm{S}\mathrm{i}\mathrm{O}}_2$) at $T=1050\mathrm{}\mathrm{K}$ show the existence of collective excitations propagating with a sound velocity of $5800\pm 200\mathrm{m}/\mathrm{s}$ up to $Q=3.5\mathrm{}{\mathrm{nm}}^{-1\mathrm{}}$. The linewidths of the excitations, which are found to obey a $Q^2$ law, are consistent with previous determinations made at low $Q$ and low $T$. The picture of the atomic dynamics in $v{-\mathrm{S}\mathrm{i}\mathrm{O}}_2$ emerging from this study indicates that these propagating modes must contribute to the boson peak.

Inelastic x-ray scattering data from water at $5°\mathrm{C}$ show a variation of the velocity of sound from 2000 to 3200 $\mathrm{m}/\mathrm{s}$ in the momentum transfer range $1–4{\mathrm{nm}}^{-1\mathrm{}}$. The transition occurs when, at $\approx 4\mathrm{meV}$, the energy of the sound excitations equals that of a second weakly dispersing mode. This mode is reminiscent of a phonon branch in ice $\mathrm{I}h$ crystals, which is shown here to be of optical transverse character. The present work accounts for most of the highly debated difference between hydrodynamic $(\approx 1500\mathrm{m}/\mathrm{s})$ and high-frequency $(\approx 3200\mathrm{m}/\mathrm{s})$ velocities of sound in water.

Exploring the dynamics of matter driven to extreme non-equilibrium states by an intense ultrashort X-ray pulse is becoming reality, thanks to the advent of free-electron laser technology that allows development of different schemes for probing the response at variable time delay with a second pulse. Here we report the generation of two-colour extreme ultraviolet pulses of controlled wavelengths, intensity and timing by seeding of high-gain harmonic generation free-electron laser with multiple independent laser pulses. The potential of this new scheme is demonstrated by the time evolution of a titanium-grating diffraction pattern, tuning the two coherent pulses to the titanium M-resonance and varying their intensities. This reveals that an intense pulse induces abrupt pattern changes on a time scale shorter than hydrodynamic expansion and ablation. This result exemplifies the essential capabilities of the jitter-free multiple-colour free-electron laser pulse sequences to study evolving states of matter with element sensitivity.