Quantum theory of light-driven coherent lattice dynamics

The exposure to intense electromagnetic radiation can induce distortions and symmetry breaking in the crystal structure of solids, providing a route for the all-optical control of their properties. In this manuscript, we formulate a unified theoretical approach to describe the coherent lattice dynamics in presence of external driving fields, electron-phonon and phonon-phonon interactions, and quantum nuclear effects. The main mechanisms for the excitation of coherent phonons - including infrared absorption, displacive excitation, inelastic stimulated Raman scattering, and ionic Raman scattering - can be seamlessly accounted for. We apply this formalism to a model consisting of two coupled phonon modes, where we illustrate the influence of quantum nuclei on structural distortions induced by ionic Raman scattering. Besides validating the widely-employed classical models for the coherent lattice dynamics, our work provides a versatile approach to methodically explore the emergence of quantum nuclear effects in the structural response of crystal lattice to strong fields.