)]$ for fixed $\omega_0$ is approximately given by $$\begin{aligned}
  \label{eq:fit_1} 
\textrm{Re} [ \sigma(\delta t , \omega_0) ] =A+B\frac{\cos(\omega_{\Delta_{\infty} }\delta t+\Phi)}{\sqrt{\delta t}}+C  \delta t ,\end{aligned}$$ as shown by the excellent fits to the numerical data in Figs. \[FigM1\](b) and \[FigM1\](c). Here, $\Phi$ is an overall phase and $A$, $B$, and $C$ are fit parameters that depend on $\omega_0$. Hence, as it is with the order parameter oscillations, oscillations in the pump-probe signal are characterized by an amplitude decaying as $1 / \sqrt{ \delta t}$ and a frequency $\omega_{\Delta_{\infty}} = 2 \Delta_{\infty} / \hbar$ that is determined by the asymptotic gap value $\Delta_{\infty} $. We note that the linear increase in the pump-probe signal of Fig. \[FigM1\](b) can be attributed to slow oscillations that are related to the finite size of the system.

We conclude that the nonadiabatic BCS state dynamics is clearly visible in $\sigma(\delta t,\omega )$ in terms of oscillations as a function of delay time $\delta t$. This is one of the key findings of the present work. The frequency dependence of the pump-probe signal, on the other hand, does not show any sign of the order parameter oscillations \[Fig. \[FigM1\](a)\] [@Papen07]. This result is in qualitative agreement with 