Stable laser control of complex multilevel systems using a weak-intensity multicolor gaussian pulse Original Research Article

The theoretical problem of the laser control of complex multilevel systems is examined, having in mind the one-photon excitation of molecules to an energy region where two adiabatic energy surfaces intersect, giving rise to ultrafast internal conversions and competing photochemical processes. The case considered here is that of a weak multicolor gaussian pulse of given duration whose frequencies correspond to the absorption lines of the system; the phases and amplitudes are taken as control parameters. The general scheme developed begins with the construction and the analysis of the subspace of states that can be prepared with a certain degree of stability and utilizes this preliminary knowledge for the search of the maximum of the selected target function. It is shown that, since the stability of the solution can be easily quantitatively estimated, one can enforce the stability requirement introducing a suitable penalty function into the target function. Examples are reported to stress that, the special care devoted to the instability problem, rarely dealt with in the literature, is of primary importance in systems exhibiting an irregular dynamics. The numerical example presented and discussed concerns the excitation by a laser pulse with a FWHM of 100 fs of a model system with two conically intersecting potential energy surfaces, and two harmonic nuclear degrees of freedom (for a total of 1200 vibronic states). The results, while illustrating the potentiality of the present approach, have also an intrinsic interest, since the field of the laser control of strongly nonadiabatic systems has been the subject of few investigations.