  We have observed cyclotron resonance in a high-mobility GaAs/AlGaAs
two-dimensional electron gas by using the techniques of terahertz time-domain
spectroscopy combined with magnetic fields. From this, we calculate the real
and imaginary parts of the diagonal elements of the magnetoconductivity tensor,
which in turn allows us to extract the concentration, effective mass, and
scattering time of the electrons in the sample. We demonstrate the utility of
ultrafast terahertz spectroscopy, which can recover the true linewidth of
cyclotron resonance in a high-mobility ($>{10}^{6} \mathrm{cm^{2} V^{-1}
s^{-1}}$) sample without being affected by the saturation effect.
