We use theory and first-principles calculations to explore mechanisms for control of the translational and point group symmetries of crystals in ultrafast optical experiments. We focus, in particular, on mechanisms that exploit anharmonic (biquadratic) lattice couplings between a driven infrared-active phonon mode and other modes at arbitrary wave vector, which are always allowed by symmetry in any space group. We use Floquet theory to develop a general phase diagram depicting the various dynamical regimes accessible to materials, with simulated dynamics to illustrate how the biquadratic coupling changes materials structures depending on both extrinsic factors (light pulse characteristics) and intrinsic materials parameters (phonon frequencies and phonon coupling strengths). We use our phase diagram, in conjunction with density functional theory calculations, both to suggest experiments to reveal hidden structural order in perovskite ${\mathrm{KTaO}}_3$ and to provide additional insights into recently reported experiments on ${\mathrm{SrTiO}}_3$ and ${\mathrm{LiNbO}}_3$.

• Received 27 April 2023
• Revised 27 August 2023
• Accepted 22 December 2023

DOI:https://doi.org/10.1103/PhysRevB.109.024110