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The macroscopic characteristics of a solid, such as its thermal, optical ortransport properties are determined by the available microscopic states aboveits lowest energy level. These slightly higher quantum states are described byelementary excitations and dictate the response of the system under externalstimuli. The spectrum of these excitations, obtained typically from inelasticneutron and x-ray scattering, is the spatial and temporal Fourier transform ofthe density-density correlation function of the system, which dictates how aperturbation propagates in space and time. As frequency-domain measurements donot generally contain phase information, time-domain measurements of thesefluctuations could yield a more direct method for investigating the excitationsof solids and their interactions both in equilibrium and far-from equilibrium.Here we show that the diffuse scattering of femtosecond x-ray pulses producedby a free electron laser (FEL) can directly measure these density-densitycorrelations due to lattice vibrations in the time domain. We obtainspectroscopic information of the lattice excitations with unprecedentedmomentum- and frequency- resolution, without resolving the energy of theoutgoing photon. Correlations are created via an acoustic analog of thedynamical Casimir effect, where a femtosecond laser pulse slightly quenches thephonon frequencies, producing pairs of squeezed phonons at momenta +q and -q.These pairs of phonons manifest as macroscopic, time-dependent coherences inthe displacement correlations that are then probed directly by x-rayscattering. Since the time-dependent correlations are preferentially created inregions of strong electron-phonon coupling, the time-resolved approach isnatural as a spectroscopic tool of low energy collective excitations in solids,and their microscopic interactions, both in linear response and beyond.

Direct measurement of time-dependent density-density correlations in a solid through the acoustic analog of the dynamical Casimir effect