The present proposal aims at a combined experimental and theoretical study of the dynamical quantum properties of phonons in crystals. The joint experimental activities in Berlin (Michael Woerner) and theoretical calculations in Luxembourg (Alexandre Tkatchenko) aim at understanding fundamental microscopic mechanisms which underlie ultrafast atomic motions and electronic charge redistribution processes in crystalline matter for which quantum properties of phonons play a significant role. Experiments and theory will focus on coherent time-dependent processes of phonons. One part of the planned activities focuses on the coherent manipulation and fully phase-resolved detection of the density matrix of multi-phonon modes in crystals using a combination of coherent n-th-order Raman excitations and coherent THz emission which allows for exciting and probing “non-classical” states in the density matrix of multi-phonon modes. Another scientific goal of this proposal is the detailed spatiotemporal characterization (with atomic length and time resolution) of the soft mode phonons in ferroelectrics and molecular crystals. In contrast to “conventional” optical phonons in crystals soft modes have a pronounced hybrid character of nuclear motions and electronic charge relocations. Multi-dimensional terahertz spectroscopy and femtosecond x-ray diffraction are the main experimental techniques of the project. Since the electronic contribution to soft-mode currents is by orders of magnitudes larger than that of the nuclei, the Born Oppenheimer approximation in a theoretical description of soft modes is no longer a good approximation because the expectation value of the kinetic energy of the nuclei contains significant inter-electronic potential surface terms. The theoretical part of this proposal which starts with a well-established background based on van der Waals inclusive density functional theory (DFT) will be explored and extended into a direction to study theoretically such “non-Born-Oppenheimer” effects of phonons crystals.