Controlling vibrational cooling with zero-width resonances: an adiabatic Floquet approach

In molecular photodissociation, some specific combinations of laser parameters (wavelength and intensity) lead to unexpected zero-width resonances (ZWRs) with, in principle, infinite lifetimes. Their potential to induce basic quenching mechanisms has recently been devised in the laser control of vibrational cooling through filtration strategies [O. Atabek et al., Phys. Rev. A 87, 031403(R) (2013)]. A full quantum adiabatic control theory based on the adiabatic Floquet Hamiltonian is developed to show how a laser pulse could be envelope-shaped and frequency-chirped so as to protect a given initial vibrational state against dissociation, taking advantage of its continuous transport on the corresponding ZWR all along the pulse duration. As compared with previous control scenarios that actually suffered from nonadiabatic contamination, drastically different and much more efficient filtration goals are achieved. A semiclassical analysis helps us to find and interpret a complete map of ZWRs in the laser parameter plane. In addition, the choice of a given ZWR path, among the complete series identified by the semiclassical approach, turns out to be crucial for the cooling scheme, targeting a single vibrational state population left at the end of the pulse, while all others have almost completely decayed. The illustrative example, which has the potential to be transposed to other diatomics, is ${\mathrm{Na}}_{2}$ prepared by photoassociation in vibrationally hot but translationally and rotationally cold states.