Proposal for laser purification in molecular vibrational cooling using zero-width resonances

Intense-field molecular photodissociation offers the possibility to define resonances of zero width for particular intensities at given wavelengths. We show how a laser pulse can be shaped to fulfill, at all times, the conditions leading to a zero width for a particular resonance originating from a field-free vibrational state. The solution of the time-dependent Schr\"odinger equation confirms that only this state survives after the pulse is off. This is the basis for a purification procedure leading to population left only in a single state chosen at will. The illustrative example is ${{\mathrm{H}}_{2}}^{+}$.