We demonstrate theoretically that laser-induced coherent quantum interference control of asymptotic states of dissociating molecules is possible – even in the (one-photon) weak-field limit starting from a single vibrational eigenstate – when resonances are in play. This is illustrated for the NaI molecule, where it is shown that the probability of observing atomic fragments as well as the distribution of their relative momenta can be changed by a phase modulated pulse with a fixed bandwidth. This type of control is restricted to finite times during the indirect fragmentation.
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