## 2 Model, Concept, Theory and Methods
### Extended Theory for the New Strategy
In the second part of Equation (50), we use the product \(\epsilon_{\pi}\tau_{\pi}\) of the field amplitude times the parameter for the duration of the \(\pi\)-pulse that yields the same result as the combined two laser pulses, i.e., complete population transfer from \(|\Psi_{g}\rangle\) to \(|\Psi_{e+}\rangle\), with transition dipole matrix elements\(d/\sqrt{2}\) and \(\langle\Psi_{g}|d_{y}|\Psi_{e+}\rangle=id/\sqrt{2}\). Using Equation (50), the concept in Equation (29) can be rewritten as the constraint between the two pulses  
\[\epsilon_{b}\tau_{b}+\epsilon_{r}\tau_{r}=\epsilon_{\pi}\tau_{\pi}. \tag{52}\]  
Since our proof-of-principle is for the special case of equal durations of the laser pulses (\(\tau_{b}=\tau_{r}=\tau_{\pi}=\tau\)), Equation (52) simplifies to the condition  
\[\epsilon_{b}+\epsilon_{r}=\epsilon_{\pi}. \tag{53}\]  
Accordingly, if the reference field amplitude of the \(\pi\)-pulse is equal to \(\epsilon_{\pi}\) and the field amplitude of the first pulse is equal to \(\epsilon_{b}\), then the second laser pulse that restores symmetry should have the same shape and the same duration as the first pulse, and its field amplitude \(\epsilon_{r}\) should \"fill the gap\" between \(\epsilon_{b}\) and \(\epsilon_{\pi}\). As a summary, Equations (50)-(53) provide the proof-of-existence for the new strategy, i.e., if the first resonant right (+) circularly polarized laser pulse with field amplitude \(\epsilon_{b}\) and with Gaussian shape function and with parameter \(\tau_{b}\) for the duration breaks the electronic structure symmetry of the ground state, then one can employ the second resonant right (+) circularly polarized laser pulse with field amplitude \(\epsilon_{r}=\epsilon_{\pi}-\epsilon_{b}\) and with Gaussian shape function with the same parameter \(\tau_{r}=\tau_{b}\) for the duration in order to restore symmetry in the electronic excited state. The success depends on the condition in Equation (33), i.e., the time delay between the laser pulses must be equal to an integer number \(N\) of the periods \(T\) of charge migration, or on the equivalent conditions in Equations (31)-(35). Finally, let us investigate the consequences for the new strategy if the conditions in Equations (31)-(35) are not satisfied, i.e., the second pulse is centered at \(t^{\prime}_{r}=t_{r}+t^{\prime}\) with time delay \(t^{\prime}_{d}=t_{d}+t^{\prime}=NT+t^{\prime}\) due to additional quasi-field-free propagation from \(t_{c}=0\) to \(t^{\prime}\). For this purpose, we employ the expression (Equation (25)) of the evolution operator \(\mathbf{U}(t^{\prime}_{f},t_{i})\) in terms of the product \(\mathbf{U}_{r}(t^{\prime}_{f},t^{\prime})\mathbf{U}_{f}(t^{\prime},t_{c}) \mathbf{U}_{b}(t_{c},t_{i})\) of the evolution operators for the first laser pulse, for quasi-field free evolution, and for the second laser pulse. In passing, this approach also yields an illuminating alternative proof of Equations (51)-(53). We need to determine the matrix representations of the time evolution operators \(\mathbf{U}_{r}(t^{\prime}_{f},t^{\prime}),\mathbf{U}_{f}(t^{\prime},t_{c})\) and \(\mathbf{U}_{b}(t_{c},t_{i})\), or in the present two-state \((g,e)\) approximation, the \(2\times 2\) matrices \(\mathbf{U}_{rge}(t^{\prime}_{f},t^{\prime}),\mathbf{U}_{fge}(t^{\prime},t_{c})\) and \(\mathbf{U}_{bge}(t_{c},t_{i})\). For this purpose, it is first helpful to determine the coefficients at the central time \(t_{c}\),  
\[