  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.
