  Light-induced ferroelectricity in quantum paraelectrics is a new avenue of
achieving dynamic stabilization of hidden orders in quantum materials. In this
work, we explore the possibility of driving transient ferroelectric phase in
the quantum paraelectric KTaO$_3$ via intense THz excitation of the soft mode.
We observe a long-lived relaxation in the THz-driven second harmonic generation
signal (SHG) that lasts up to 20 ps at 10 K which may be attributed to
light-induced ferroelectricity. Through analyzing the THz-induced coherent
soft-mode oscillation and finding its hardening with fluence well described by
a single well potential, we demonstrate intense THz pulses up to 500 kV/cm
cannot drive a global ferroelectric phase in KTaO$_3$. Instead, we find the
unusual long-lived relaxation of SHG comes from a THz-driven moderate dipolar
correlation between the defect-induced local polar structures. We discuss the
impact of our findings on current investigations of the THz-induced
ferroelectric phase in quantum paraelectrics.
