## 7 Discussion and Conclusions  
The numerical calculations reported in this work produced two major results. The first one is the clear enhancement of population and vibrational coherence for near-resonant excitation obtained by using chirped laser pulses (Figure 5a,b,e,f). The enhancement of the population and the vibrational coherences in the upper and ground states differ, though, in the sign of the chirp and the direction of the detuning. While population transfer due to pump-dump processes from the ground and back to the ground states is maximized for negative chirp, when the laser is tuned near the lowest upper vibrational state (level \(|3\rangle\)), enhancement of the population in the excited states is obtained both for positive and negative chirps, with a central laser wavelength slightly tuned above the upper vibrational states. The simulations show that the enhancement of the ground vibrational states is obtained by negatively chirped pulses slightly tuned above and below level \(|3\rangle\), while the enhancement of the excited state vibrations is observed in a tiny region with both positive and negative small chirps and the laser slightly tuned below level \(|3\rangle\).  
The second major result is the absence of population enhancement in the upper states using chirped pulses, when their spectra are resonant with the transition (Figure 5e,f). Also important is the lack of any substantial change in the population enhancement with resonant chirped pulses when molecular electronic dephasing is increased to 200 fs (Figure 7c). This clearly indicates how robust this result is for a wide range of molecular systems. Perhaps even more importantly, our finding hints at why coherent control experiments of photochemical reactions in electronic excited states, which often use electronic resonant tailored excitations, have been challenging in many cases [67; 68; 69].  
In conclusion, we have performed a numerical study on coherent control via chirped pulses in a four-level system by considering specific parameters typical of oxazine systems. We have studied in detail the influence of the detuning of the laser input pulse with respect to the electronic transitions. We have evaluated in some particular cases the effect of the duration of the laser pulse, its peak intensity, and also the influence of the electronic dephasing. We conclude that the time ordering of frequencies inside a pulse makes a fundamental difference in the population transfer and vibrational coherence generation, which can be computed with our four-level model. Intra-pulse adiabatic mechanisms explain most of the enhancement effects that we have observed. Although the results that we have presented are obtained for specific parameter values, the numerical model that we have studied is sufficiently simple to allow for an extension of our findings to other systems. An advance in the understanding of these light-matter interaction processes could open up new pathways and ideas in the field of nonlinear quantum control spectroscopy [70].  
We are grateful to [PERSON] for careful reading of the manuscript. Support from the Spanish Ministry of Economy and Competitiveness through FIS2014-51997-R is acknowledged.  
[PERSON] and [PERSON] conceived and designed the simulations, and wrote the paper.  
The authors declare no conflict of interest.