A Microscopic Description of Displacive Coherent Phonons

We develop a Hamiltonian-based microscopic description of laser pump induced displacive coherent phonons. The theory captures the feedback of the phonon excitation upon the electronic fluid, which is missing in the state-of-the-art phenomenological formulation. We show that this feedback leads to chirping at short time scales, even if the phonon motion is harmonic. At long times this feedback appears as a finite phase in the oscillatory signal. We apply the theory to BaFe$_2$As$_2$, explain the origin of the phase in the oscillatory signal reported in recent experiments, and we predict that the system will exhibit red-shifted chirping at larger fluence. Our theory also opens the possibility to extract equilibrium information from coherent phonon dynamics.