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 timescales, 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 ${\mathrm{BaFe}}₂{\mathrm{As}}₂$, explain the origin of the phase in the oscillatory signal reported in recent experiments, and we predict that the system will exhibit redshifted chirping at larger fluence. Our theory also opens the possibility to extract equilibrium information from coherent phonon dynamics.