Kapitza stabilization of quantum critical order

Dynamical perturbations modify the states of classical systems in surprising ways and give rise to important applications in science and technology. For example, Floquet engineering exploits the possibility of band formation in the frequency domain when a strong, periodic variation is imposed on parameters such as spring constants. We describe here Kapitza engineering, where a drive field oscillating at a frequency much higher than the characteristic frequencies for the linear response of a system changes the potential energy surface so much that maxima found at equilibrium become local minima, in precise analogy to the celebrated Kapitza pendulum where the unstable inverted configuration, with the mass above rather than below the fulcrum, actually becomes stable. Our starting point is a quantum field theory of the Ginzburg-Devonshire type, suitable for many condensed matter systems, including particularly ferroelectrics and quantum paralectrics such as the common substrate (for oxide electronics) strontium titanate (STO). We show that an off-resonance oscillatory electric field generated by a laser-driven THz source can induce ferroelectric order in the quantum-critical limit. Heating effects are estimated to be manageable using pulsed radiation; "hidden" radiation-induced order can persist to low temperatures without further pumping due to stabilization by strain. We estimate the Ginzburg-Devonshire free-energy coefficients in STO using density functional theory (DFT) and the stochastic self-consistent harmonic approximation accelerated by a machine learned force field. Although we find that STO is not an optimal choice for Kapitza stabilization, we show that scanning for further candidate materials can be performed at the computationally convenient density functional theory level. We suggest second-harmonic-generation, soft-mode-spectroscopy, and X-ray-diffraction experiments to characterize the induced order. This Materials Cloud entry contains the DFT calculations, the force field and results from SSCHA calculations used in the article.