Laser cooling of the vibrational motion of Na{sub 2} combining the effects of zero-width resonances and exceptional points

We propose various scenarios for molecular vibrational cooling combining the effects of two kinds of resonance states occurring during the photodissociation of Na{sub 2} taken as an illustrative example. Such resonances result from an appropriate sampling of laser parameters (wavelength and intensity): (a) For particular choices of intensity and wavelength, two resonance energies can be brought to complete coalescence, with their positions and widths becoming equal and leading to a so-called exceptional point (EP) in the parameter plane. Advantage can be taken from such points for very selective laser-controlled vibrational transfer strategies. (b) For specific intensities, far beyond the perturbation regime, some resonances can have a zero width (infinite lifetime). They are referred to as a zero-width resonance (ZWR) and may be used for vibrational purification purposes. We show how appropriately shaped, experimentally reachable laser pulses, encircling EPs or inducing ZWRs, may be used for a thorough and comprehensive control aiming at population transfer or purification schemes, which, starting from an initial field-free vibrational distribution, ends up in the ground vibrational level.