and positive pump-probe delay times $\delta t$, depending on whether the probe pulse precedes the pump pulse ($\delta t<0$) or follows after it ($\delta t>0$). For the numerical computations we assume that the pump pulse is centered in time at $t=0$ ps and has photon energy $\hbar\omega_{\text{p}}=3$ meV, which is slightly larger than twice the gap energy $2 | \Delta (t_{\textrm{i}} )  |$ of the superconductor in the initial state at $t=t_{\textrm{i}}$. The probe pulse is taken to be very short in time with FWHM $\tau_{\text{pr}}=0.25$ ps and center energy $\hbar\omega_{\text{pr}}=2.5$ meV (see Fig. \[FigM9\_new\] in Appendix \[sec:eom\]).

Thus, the probe pulse contains a broad range of frequencies which cover almost the entire energy range of excited quasiparticles induced by the pump pulse similar to recent experiments [@DalScience2013; @matsunagaPRL12; @matsunagaPRL13]. Nonlinear couplings between the superconductor and the probe pulse are neglected because probing is done with much weaker intensity in the linear response regime.

Equations of motion {#sec:method}
===================

In order to simulate the pump-probe conductivity, we need to determine the temporal evolution of the electric current density ${\bf j}_{{\bf q}_{\textrm{pr}}} (\delta t, t)$, where ${\bf q}_{\textrm{pr}}= \left| {\bf q}_{\textrm{pr}} \right| \hat{{\bf e}}_x$ is the wave vector of the probe 