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The constraint of time-integrated zero-area on the laser field is afundamental, both theoretical and experimental requirement in the control ofmolecular dynamics. By using techniques of local and optimal control theory, weshow how to enforce this constraint on two benchmark control problems, namelymolecular orientation and photofragmentation. The origin and the physicalimplications on the dynamics of this zero-area control field are discussed.

Control of molecular dynamics with zero-area fields: Application to molecular orientation and photofragmentation