  The gain recovery time of a heterogeneous active region terahertz quantum
cascade laser is studied by terahertz-pump,i terahertz-probe spectroscopy. The
investigated active region, which is based on a bound-to-continuum optical
transition with an optical phonon assisted extraction, exhibits a gain recovery
time in the range of 34$\,$-$\,$50$\,$ps dependent on the operation condition
of the laser. The recovery time gets shorter for stronger pumping of the laser
while the recovery dynamics slows down with increasing operation temperature.
These results indicate the important role of the intracavity light intensity
for the fast gain recovery.
