Abstract: Controlling phases of matter with light is a central goal in condensed matter physics. I will present new theories of light–matter interaction that show how light shapes and drives instabilities in quantum materials across electronic, structural, and collective-mode sectors. First, I show that resonant optical absorption can drive layer sliding in van der Waals flakes (e.g. in CrI3, MoTe2, MoSe2) via nonlinear light–matter coupling. The effect is governed by the quantum geometry of Bloch states through the time-dependent Quantum Geometric Tensor (tQGT), derived within time-dependent Kohn–Sham theory.
Second, I demonstrate that light can dynamically generate the nonlinearities underlying incommensurate structural transitions, with an unexpected analogy to Faraday waves. For systems with continuous symmetry breaking (e.g., incommensurate charge density waves), light couples amplitude (Higgs) and phase (Goldstone) modes. Driving the amplitude mode out of equilibrium (above a threshold) induces resonant parametric down-conversion into Goldstone modes, thus leading to Faraday-Goldstone waves. This produces long-lived spatiotemporal order with a wavevector set by the drive rather than the equilibrium order, which is surprisingly robust to temperature and disorder. I outline how the relevant nonlinear couplings can be computed from first principles (e.g., DFT). I will present experimental evidence for this effect in K_{0.3}MnO_{3} (blue bronze).
Finally, I introduce Machine Learning-assisted electronic structure modeling of incommensurate bilayers: Using DFT, Wannier-based tight-binding models are generated for arbitrary local stackings. These tight-binding models are extrapolated for arbitrary stacking by optimized Random Forest (RF) regression which interpolates over chemical environments. As a direct application, I will show an improved Kernel Polynomial Method that yields the DOS of incommensurate bilayers 20 times faster (compared with plane-wave DFT calculations), with new predictions for twistable materials exhibiting enhanced DOS. I conclude with prospects for light-driven phases of matter in both fundamental physics and technological applications.