Fig. \[FigM3\](c)\]. In other words, it is found that for these absorption energies $\textrm{Re} [ \sigma(\delta t , \omega )]$ oscillates in $\delta t$ with three frequencies that are approximately given by $\omega_{\Delta (t_i)}$, $\omega_{\Delta (t_i)} + \omega $, and $\omega_{\Delta (t_i)} - \omega $.

![image](Fig_5a){width="\columnwidth"} ![image](Fig_5b){width="\columnwidth"}

Pump-probe response in the presence of an optical phonon mode {#sec:Results_zwei}
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![ \[FigM6\] \[plot:sigma-rg3\] (Color online) (a) Absorption spectrum $\textrm{Re} [ \sigma(\delta t,\omega) ]$ versus $\omega$ and $\delta t > 0$ for the adiabatic regime \[$\tau_{\textrm{p}}=20$ ps, $|\textbf{A}_{\textrm{p}}|=0.5\cdot10^{-8}$ Js/(Cm)\] in the presence of an optical phonon mode with energy $\hbar \omega = 2$ meV and coupling strength $g_{\text{ph}}=0.1$ meV. (b), (c) Time dependence of the order parameter amplitude $| \Delta (t) |$ and the lattice displacement $U(0,t)$, respectively, for the same parameters as in panel (a). (d) Spectral distribution of the coherent phonon oscillations. ](Fig_6){width="\columnwidth"}

![ \[FigM8a\] (Color online) (a) Real part of the pump-probe signal, $\textrm{Re} [ \sigma(\delta t,\omega) ]$, versus $\omega$ and $\delta t > 0$ for the adiabatic regime \[$\tau_{\textrm{p}}=20$ ps, $|\textbf{A}_{\textrm{p}}|=0.5\cdot10^{-8}$ Js/(Cm)\] in the presence of an optical phonon mode that is in resonance with pump pulse energy, i.e., $\hbar \omega_{\textrm{ph}} = \hbar \omega_{\textrm{p}} = 3$ meV. The 