## 3 Main Results Obtained from the Simulations
Figure 3a shows how the maximum enhancement obtained for negatively chirped pulses at 18,800 cm\({}^{-1}\) presents an oscillatory behavior of \(\rho_{11}+\rho_{22}\), while the TL pulse at this wavenumber induces a pump-dump scenario. Note that the transferred population is small at this detuning (\(\simeq\)5%). This behavior is qualitatively different from the more resonant cases in Figure 3b,c, where the pump-dump processes are not that clear and the population transfers become \(\simeq\)40%. 2. Coherence in the ground state \(\mid\!\!\rho_{12}\!\mid\): The highest enhancement of the coherence in the ground state is \(\simeq\)1.35 and is obtained at a negative chirp of \(\Phi^{\prime\prime}\simeq-430\) fs\({}^{2}\) and at the excitation wavenumbers of \(\widetilde{v}\simeq\) 19,660 cm\({}^{-1}\) and \(\widetilde{v}\simeq\) 19,150 cm\({}^{-1}\) (see Figure 2b). The enhancement of the vibrational coherence in the ground states therefore responds basically to the same phenomena that the one for the ground state population, i.e., the pump-dump intra-pulse mechanisms are promoted for negatively chirped pulses and suppressed for positive chirp. The details of the precise values of the two central laser pulse wavenumbers that produce the maximum enhancement are intriguing intra-pulse mechanisms which have not been clarified completely. Our result is in accordance with the studies made in [60], where it is observed for oxazine 1 systems in ethanol that ground-state vibrational coherences are enhanced predominantly by negatively chirped pulses. Figure 4 shows the evolution in time of the coherences at some specific values of the central laser  
Figure 3: Time evolution of the populations in the ground state (**a–c**); and in the upper states (**d–f**); for specific parameter values, as indicated. Note that the lines, which are named with letters, correspond to the parameter values detailed in Figure 5a,e. pulse wavenumber and chirp. In Figure 4a the time evolution of the vibrational coherence in the ground states for the two different wave numbers that produce enhancement at negative chirp can be seen, and also the reduction of the coherence \(\mid\!\rho_{12}\!\mid\) after the interaction of the first half of the pulse in the case of positively chirped pulses. 3. Population in the upper states (\(\rho_{33}+\rho_{44}\)): Figure 2c shows that the peak enhancement in population transfer to the upper states is \(\simeq\)1.23 at the chirp values \(\phi^{\prime\prime}=\pm 10^{3}\) fs\({}^{2}\) and for an excitation wave number of \(\widetilde{v}\simeq\) 20,550 cm\({}^{-1}\). A qualitatively different smaller enhancement of \(\simeq\)1.1 is also obtained at the positive chirp \(\phi^{\prime\prime}=260\) fs\({}^{2}\) and for an excitation wave number of \(\widetilde{v}\simeq\) 18,840 cm\({}^{-1}\). The highest suppression is obtained at a close wave number of \(\widetilde{v}\simeq\) 18,920 cm\({}^{-1}\) for a negative chirp of \(\phi^{\prime\prime}=-10^{3}\) fs\({}^{2}\). On the one hand, the symmetric enhancement with respect to chirp at \(\widetilde{v}\simeq\) 20,550 cm\({}^{-1}\) can be understood by the evolution in time of the population in the upper states for the TL and the chirped pulses at this particular central laser pulse wavenumber, in Figure 3f. The behavior can be seen as the opposite to the effect in the ground state and for red detuned pulses (Figure 3a). In this case the oscillatory behavior corresponds to the positively chirped pulse. On the other hand, the enhancement obtained for red detuned pulses at \(\widetilde{v}\simeq\) 18,800 cm\({}^{-1}\) is the consequence of an optimized pump-dump transition, as shown in Figure 3d, which as opposed to the enhancement of the population in the ground state, it is favored by positively chirped pulses, as was also observed in [57; 58; 59]. 4.