Advances in mid and far-infrared THz sources have created a new paradigm in condensed matter physics: ultrafast structural and functional control through direct lattice excitation. Striking changes in magnetism, metallicity, ferroelectricity, and superconductivity, observed experimentally on ultrafast timescales, have been tied to the anharmonic coupling between pumped infrared-active (IR) phonons and Raman-active phonons via the nonlinear phononics effect. This nonlinear phononics pathway elevates coupling between two zero-wavevector phonons – the IR and Raman phonons – above the vast scattering phase space allowed in the Brillouin zone of crystalline materials.
 
In our theoretical exploration of energy transfer from large amplitude excitations of IR phonons we have found that strong coupling to non-zero wavevector phonons – those that are not optically active – is common and can dominate the lattice response, even condensing to form new nonequilibrium phases periodically modulated on extended length scales. Here we use a combination of Floquet and first-principles theory, and dynamical simulation to expand the nonlinear phononics perspective to the coherent control of point group and translational symmetry of crystalline materials with light, while unifying nonlinear phononics with several concepts from the study of dynamical systems.