  I propose a method for ultrafast switching of ferroelectric polarization
using mid-infrared pulses. This involves selectively exciting the highest
frequency $A_1$ phonon mode of a ferroelectric material with an intense
mid-infrared pulse. Large amplitude oscillations of this mode provides a
unidirectional force to the lattice such that it displaces along the lowest
frequency $A_1$ phonon mode coordinate because of a nonlinear coupling of the
type $g Q_{\textrm{P}} Q_{\textrm{IR}}^2$ between the two modes. First
principles calculations show that this coupling is large in transition-metal
oxide ferroelectrics, and the sign of the coupling is such that the lattice
displaces in the switching direction. Furthermore, I find that the lowest
frequency $A_1$ mode has a large $Q_{\textrm{P}}^3$ order anharmonicity, which
causes a discontinuous switch of electric polarization as the pump amplitude is
continuously increased.
