  We develop a theory for the nonlinear time domain response of a Weyl
semimetal driven by an ultrafast optical pulse. At quadratic order in the
driving field we find that the response near a band inversion transition
contains a coherent oscillating component proportional field intensity and with
a frequency that can be tuned over a wide range (from THz to the near IR)
selected by the chemical potential. We illustrate the effect by calculating the
induced current as a function of time for a model of a parity broken Weyl
semimetal where large Berry curvature near the band inversion transition
promotes this nonlinear response.
