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 $l$ 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$_3$ by a midinfrared pulse with a peak electric field of 17 MV cm$^{-1}$ 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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