## 3 Main Results Obtained from the Simulations
For the values of the peak field amplitude and dipole coupling that we have considered, the period associated to the Rabi oscillations is \(T_{\rm Rabi}=h/(\mathfrak{u}E)\simeq 180\) fs. Also important is the spectral width of the 30 fs Gaussian laser pulse, which is \(0.441/(\mathfrak{ct}_{\rm p})\simeq 490\) cm\({}^{-1}\), which is to be compared with the 600 cm\({}^{-1}\) of the vibrations considered in our simulations. The fastest dephasing rate in the simulations shown in Figure 2 is 100 fs, which therefore allows in this case for purely coherent processes, since all the interaction is basically finished before that time. We study the influence of the dephasing rates on the enhancement effects in the last part of the paper. We next describe in detail and provide an interpretation of the main results shown in Figure 2.  
(1) Population in the ground state (\(\rho 11+\rho 22\)):  
The peak enhancement of the population in the ground state (Figure 2a) is \(\simeq\) 1.073 at a chirp value of \(\phi^{\prime\prime}=-10^{3}\) fs\({}^{2}\) and for an excitation wave number of \(\tilde{\upsilon}\simeq\) 19,520 cm\({}^{-1}\), which is red-detuned and close to the resonance of the first upper vibrational state at \(\tilde{\upsilon}=\) 19,400 cm\({}^{-1}\). The highest suppression is obtained at a chirp of \(10^{3}\) fs\({}^{2}\) with a laser central wavenumber of \(\tilde{\upsilon}\simeq\) 20,320 cm\({}^{-1}\), which is blue-detuned to the resonance of the second upper vibrational state at \(\tilde{\upsilon}=\) 20,000 cm\({}^{-1}\). The asymmetry of the enhancement with respect to the sign of the chirp can be understood as follows. The first half of the interacting laser pulse promotes population inversion, which can be available for stimulated emission depending on the shape of the laser pulse and its spectral components. In the case of the highest enhancement of the population \(\rho_{11}+\rho_{22}\), for instance, if we consider that the upper state is first excited at a wave number at \(\tilde{\upsilon}\simeq\) 19,765 cm\({}^{-1}\), which corresponds to the beginning of the laser pulse, a vibrational wave packet will be created in the upper state, which will initiate its oscillation between the upper state vibrational sublevels at this particular frequency. The round trip of the wave packet to the highest vibrational level at \(\tilde{\upsilon}=\) 20,000 cm\({}^{-1}\) and back to \(\tilde{\upsilon}\simeq\) 19,765 cm\({}^{-1}\) will take about 23.5 fs. From that time, the resonant  
Figure 2: Enhancement/suppression factor of (**a**) population in the ground state; (**b**) vibrational coherence in the ground state; (**c**) population in the upper state; and (**d**) vibrational coherence in the upper state. Dashed lines indicate the position of the excited states (see Figure 1). transitions of the excited atom or molecule available for stimulated emission will be smaller than 19,765 cm\({}^{-1}\), and therefore the red shifted frequencies of the negatively chirped laser pulse will meet them and stimulated transfer back to the ground state will be promoted. This is therefore an adiabatic intra-pulse pump-dump scenario that explains the enhancement observed for negatively chirped pulses. For a laser pulse positively chirped, e.g., at this same central pulse frequency of 19,520 cm\({}^{-1}\), however, the later higher frequencies of the pulse cannot promote the system down and will instead continue exciting the system to the upper states. Consequently, the population of the ground state when the laser pulse is gone is not enhanced for positively chirped pulses, as it can be seen in Figure 2a. The results that we obtain with our simple four-level system are therefore fully corroborated by the previous theoretical studies and experimental measurements [61; 62; 63]. In Figure 3 we have plotted the evolution in time of the populations at some specific values of the central laser pulse wavenumber and chirp.