  Harmonic generation provides an efficient tool for the study of ultrafast
nonlinear dynamics. We report on time-resolved optical-pump
terahertz-harmonic-generation spectroscopic investigation of ultrafast
nonlinearity in a prototypical three-dimensional Dirac semimetal Cd$_3$As$_2$.
A transient population inversion characterized by excessive nonthermal Dirac
electrons and holes is found to be very sensitive and responsive to a periodic
terahertz drive, leading to very efficient terahertz third-harmonic generation.
Based on the Boltzmann transport theory, we analyze the terahertz field-driven
kinetics of the transient Dirac fermions that is responsible for the observed
strong terahertz nonlinearity.
