## 3 Results and Discussion
Note that the labels in the vertical axis of (**a**) indicate a logarithmic scale. The physical mechanism by which the optimal pulse is achieved, and in particular how much of the ionization in the process is due to tunneling, considering a tiny change in the electric field of the IR pulse, how much is due to ionization caused by the XUV\({}_{1}\) field, or by the effect of time modulation of the atomic potential and bound wave function is difficult to elucidate. However, some insight of the physics behind the described process can be obtained. Figure 2b shows how the optimal position at which the XUV\({}_{1}\) pulse is added lies in the temporal late wing of the IR pulse, which in this case corresponds to \(\theta=718^{\circ}\). Also, the inset in Figure 2b shows the amplitude of the XUV\({}_{1}\) pulse near the center of the IR pulse. Observing the reduction of the intensity generated in the HHG process from the central part of the IR pulse (Figure 2d), we can conclude that the small perturbations in the center of the IR pulse caused by the early wing of the XUV\({}_{1}\) pulse induce a phase reshaping in the HHG quantum trajectories that result in a strong cancellation of the HHG signal. This conjecture is supported by the fact that small variations on the amplitude of the IR field can produce a substantial change on the phase of the quantum trajectories, as it is described in detail in [20], and also by an analysis of the mostly contributing trajectories that will be shown below. In the present case we hence observe that a flattening of the spectral amplitude involves a synchronization of the phases in the quantum trajectories participating in the HHG process, so that the overall spectral phase results optimally changed. As it is shown in the inset of Figure 2d, the spectral phase of the spectrum is indeed substantially modified by the optimization process. As commented above, an additional insight on the contribution of the two main electron trajectories involved in the HHG generation process can be obtained by an study of the time distribution of the energy in the spectrum, which is shown in Figure 3. Although the resolution of the figure is not optimal due to limitations from the numerical simulations, the cycles in the photon energy versus time plane, which correspond to the time-dependent intensity profile of the IR pulse, can still be well recognized. Indeed, each cycle accords to half period of the driving IR pulse, with the earlier half of each cycle showing the first occurring recollisions (short trajectories) and the second half showing the contribution of the long trajectories. The duration of the two trajectories coincides in the cutoff, where the highest photon energies are generated. Only qualitative results are shown in Figure 3 for clarity, with a more intense red color indicating a higher harmonics yield. In Figure 3a the original unperturbed spectrum shows an obvious symmetry. The spectrum in Figure 3b, which corresponds to the optimized case, shows two important features: first, there is not a selection of a particular trajectory in the central part of the IR pulse, which supports that a destructive interference between the short and long trajectories is produced in this region due to variations in their relative phase. Second, the perturbation produced by the XUV\({}_{1}\) pulse in the late wing of the IR pulse induces an enhancement of the signal in the spectral region that is optimized (21-51 eV) together with a suppression of the contribution of the long trajectories in that region, which is a relevant consequence of the optimization procedure. The overall effect is a confinement of the HHG signal at \(\approx\) 5 fs ahead from the peak of the IR pulse, which results in an almost isolated attosecond pulse (see Figure 2d).