Coherent control of radiationless transitions: simultaneous excitation and decay of overlapping resonances

We develop a simple analytical theory for the study of coherent control of radiationless transitions, and in particular, internal conversion leading to dissociation, in molecules possessing overlapping resonances. The method is applied to a model diatomic system. In contrast to previous studies, we consider here the control of a molecule that is allowed to decay during and after the preparation process. We use this theory to derive the shape of the laser pulse that creates the specific excited wave packet that best enhances or suppresses the radiationless transitions process. The results show the importance of resonance overlap in the molecule in order to achieve efficient coherent control over radiationless transitions via laser excitation. Specifically, resonance overlap is proven to be crucial in order to alter interference contributions to the controlled observable, and hence to achieve efficient coherent control by varying the phase of the laser field.