## 4 Conclusions  
This paper presents a new strategy for the restoration of the symmetry of electronic structure by means of a well-designed laser pulse, after symmetry was broken by a first laser pulse, which excites the electronic ground state to a superposition of the ground state and an excited state with different \(IRREPs\). The superposition state is non-stationary; it represents periodic charge migration with period \(T\). Typical values of \(T\) for electronic superposition states are in the time domain from several hundred attoseconds to few femtoseconds. Symmetry is restored by the second laser pulse, which excites the superposition state to the excited state. The net effect of the two laser pulses can be summarized as an excitation of the electronic ground state to the excited state, with \(IRREP_{e}\
eq IRREP_{g}\). This observation suggests that, as a necessary condition for this new type of symmetry restoration, the second laser pulse must be designed such that the sum of the first and second laser pulses add up to a \(\pi\)-pulse. There are many ways to satisfy this condition. In the present application to the model benzene, both laser pulses are designed as circularly right (+) polarized laser pulses, with the same Gaussian shapes, the same parameters for the duration, the same resonant carrier frequencies, the same carrier envelope phases, but with two different temporal centers and with different field strengths. Specifically, the time delay between the temporal centers of the two laser pulses must be equal to an integer number of periods \(T\). This condition must be satisfied with precision of few attoseconds. The experimental feasibility of this high accuracy is demonstrated in Ref. [19]. The condition for the field strength of the second laser pulse is that the sum of the field strengths of the first and second laser pulses must add up to the field strength of the circularly polarized \(\pi\)-pulse that otherwise has the same parameters as the first and second pulses. One may thus consider the two laser pulses as \"fractional \(\pi\)-pulses\". Previously, it has been shown that fractional \(\pi\)-pulses are useful for other purposes as well, e.g., for laser generation of hybrid orbitals[47]. The present proof-of-principle of the new strategy, together with the alternative previous strategies [19; 20; 21], should stimulate the search for alternative approaches to laser symmetry restoration. As a working hypothesis, the present concept should allow several extensions, e.g., the fractional \(\pi\)-pulse for symmetry restoration may be designed with weaker or stronger field strengths that are compensated by longer or shorter duration, respectively, or one might employ the carrier envelope phase as a control knob in order to compensate the effect of time delays with non-integer multiples of the period \(T\). By extrapolation of the concept and derivations of this manuscript, the field of laser symmetry breaking and restoration leads into new territories of research that allow rich discoveries. From the experimental point of view, one should keep in mind that the present new concept of laser control from symmetry breaking via charge migration to symmetry restoration is general and should apply to many other rigid molecules--the present example of the benzene molecule should stimulate the search for candidates with more suitable parameters for experimental verification. [PERSON] and [PERSON] proposed the new strategy of quantum control of electronic structure symmetry breaking and restoration; [PERSON] discovered the concept, derived most part of the theory and wrote the zero order draft; and [PERSON] obtained the important Equation (62), carried out all the quantum dynamics simulations and prepared the figures (the snapshots of the one-electron densities were plotted by [PERSON]). All co-authors together prepared the final version of the manuscript. This work profited from financial support in part by the National Key Research and Development Program of China (No.