equations  for finite electron-phonon coupling $g_{\textrm{ph}}$. The correlation expansion used to derive the equations of motion of the coupled Bogoliubov quasiparticle-phonon system is valid as long as $g_{\textrm{ph}}$ is smaller than the superconducting energy scales. Hence, for the numerical calculations we take $g_{\textrm{ph}} = 0.1$ meV $\ll \Delta ( t_i )$, in which case the influence of the phonon subsystem on the superconductor becomes negligibly small. As in the previous section, we focus on ultrashort pump pulses with $\tau_{\textrm{p}} \ll \tau_{\textrm{ph}}, \tau_{\Delta}$ that drive both the quasiparticle and the phonon subsystems in a nonadiabatic fashion.

Positive pump-probe delay time
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First, we examine the results for positive pump-probe delay time, where the probe pulse follows the pump pulse after the delay time $\delta t >0$.

### Nonadiabatic regime, $\tau_{\textrm{p}} \ll \tau_{\textrm{ph}}  \approx  \tau_{\Delta}$ {#posTnonAdia}

The most interesting case corresponds to the situation where an ultrashort pump pulse drives quasiparticle oscillations with a frequency that is close to resonance with the phonon energy, i.e., $\tau_{\textrm{p}}  \ll \tau_{\textrm{ph}}  \approx  \tau_{\Delta}$, see Figs. \[FigM4\], \[FigM5\], and \[FigM12\]. Figure \[FigM4\](a) displays the real part of the pump-probe signal as a function of delay time and frequency for a pump pulse with width $\tau_{\textrm{p}}=0.5$ ps 