  A non-equilibrium theory of optical conductivity of dirty-limit
superconductors and commensurate charge density wave is presented. We discuss
the current response to different experimentally relevant light-field probe
pulses and show that a single frequency definition of the optical conductivity
$\sigma(\omega)\equiv j(\omega)/E(\omega)$ is difficult to interpret out of the
adiabatic limit. We identify characteristic time domain signatures
distinguishing between superconducting, normal metal and charge density wave
states. We also suggest a route to directly address the instantaneous
superfluid stiffness of a superconductor by shaping the probe light field.
