I show that a nonequilibrium paraelectric to ferroelectric transition can be induced using midinfrared pulses. This relies on a quartic lQ_{\textrm{l_z}}^2Q_{\textrm{h_x}}^2 coupling between the lowest (Q_{\textrm{l_z}}) and highest (Q_{\textrm{h_x}}) frequency infrared-active phonon modes of a paraelectric material. Density functional calculations show that the coupling constant is negative, which causes a softening of the Q_{\textrm{l_z}} mode when the Q_{\textrm{h_x}} mode is externally pumped. A rectification along the Q_{\textrm{l_z}} coordinate that stabilizes the nonequilibrium ferroelectric state occurs only above a critical threshold for the electric field of the pump pulse, demonstrating that this is a nonperturbative phenomenon. A first principles calculation of the coupling between light and the Q_{\textrm{h_x}} mode shows that ferroelectricity can be induced in the representative case of strained KTaO by a midinfrared pulse with a peak electric field of 17 MV cm and duration of 2 ps. Furthermore, other odd-order nonlinear couplings make it possible to arbitrarily switch off the light-induced ferroelectric state, making this technique feasible for all-optic devices.

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