Recent experiments have demonstrated that intense terahertz (THz) fields can induce a transition from the quantum paraeletric to the ferroeletric phase of SrTiO$_3$. Here, we investigate this THz field-induced transient ferroeletric phase transition by solving the time-dependent lattice Schodinger equation based on first-principles calculations. We find that transient ferroeletricity originates from a light-induced mixing between ground and first excited lattice states in the quantum paraeletric phase. In agreement with the experimental findings, our study shows that the non-oscillatory second harmonic generation signal can be evidence of transient ferroeletricity in SrTiO$_3$. We reveal the microscopic details of this exotic phase transition and highlight that this phenomenon is a unique behavior of the quantum paraeletric phase.
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