  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.
