Resonant squeezing and the anharmonic decay of coherent phonons

We show that the anharmonic decay of large-amplitude coherent phonons in a solid generates strongly enhanced squeezing of the phonon modes near points of the Brillouin zone where energy conservation in the three-phonon decay process is satisfied. The squeezing process leads to temporal oscillations of the mean-square displacement of target modes in resonance with the coherent phonon, which are characteristic of coherent phonon decay and do not occur in the decay of a phonon in a well-defined number state. For realistic material parameters of optically excited group-V semimetals, we predict that this squeezing results in strongly enhanced oscillations of the x-ray diffuse scattering intensity at sharply defined values of the x-ray momentum transfer. Numerical simulations of the phonon dynamics and the x-ray diffuse scattering in optically excited bismuth, using harmonic and anharmonic force parameters calculated with constrained density functional theory, demonstrate oscillations of the diffuse scattering intensity of magnitude 10%--20% of the thermal background at points of the Brillouin zone, where resonance occurs. Such oscillations should be observable using time-resolved optical-pump and x-ray-probe facilities available at current x-ray free-electron laser sources.