  Time-resolved terahertz time-domain spectroscopy (THz-TDS) is an ideal tool
for probing photoinduced nonequilibrium metallic and superconducting states.
Here, we focus on the interpretation of the two-dimensional response function
$\Sigma(\omega;t)$ that it measures, examining whether it provides an accurate
snapshot of the instantaneous optical conductivity, $\sigma(\omega;t)$. For the
Drude model with a time-dependent carrier density, we show that
$\Sigma(\omega;t)$ is not simply related to $\sigma(\omega;t)$. The difference
in the two response functions is most pronounced when the momentum relaxation
rate of photocarriers is long, as would be the case in a system that becomes
superconducting following pulsed photoexcitation. From the analysis of our
model, we identify signatures of photoinduced superconductivity that could be
seen by time-resolved THz-TDS.
