Direct Measurement of Anharmonic Decay Channels of a Coherent Phonon

We report channel-resolved measurements of the anharmonic coupling of the coherent A_{1g} phonon in photoexcited bismuth to pairs of high wave vector acoustic phonons. The decay of a coherent phonon can be understood as a parametric resonance process whereby the atomic displacement periodically modulates the frequency of a broad continuum of modes. This coupling drives temporal oscillations in the phonon mean-square displacements at the A_{1g} frequency that are observed across the Brillouin zone by femtosecond x-ray diffuse scattering. We extract anharmonic coupling constants between the A_{1g} and several representative decay channels that are within an order of magnitude of density functional perturbation theory calculations.