Multiple occurrence of zero-width resonances in photodissociation: Effect of laser field intensity and frequency

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Critical intensities at which the strong field photodissociation rates of a molecule are vanishing could play an important role in control scenarios to filter a given vibrational state. We have previously shown [O. Atabek, R. Lefebvre, and F. Gad\'ea, Phys. Rev. A 74, 063412 (2006)] that there is a multiplicity of such intensities when the diabatic curve crossing point is on the left of the minimum of the attractive potential in a photon dressed picture (${c}^{\ensuremath{-}}$ case). A semiclassical explanation was given. We complete this study of the multiple occurrence of zero-width resonances (ZWRs) by addressing, both numerically and semiclassically, the more common ${c}^{+}$ case of a crossing point on the right of the potential minimum. Coincidences between modified diabatic and adiabatic levels are the fingerprints of such events. They occur several times because the adiabatic energies are moving upward more rapidly than the diabatic ones. Advantage can be taken of the frequency dependence of the critical intensities to produce the phenomenon even for weak fields, this circumstance leading to more favorable control issues. This is illustrated on the example of ${\mathrm{H}}_{2}^{+}$. The wave functions associated with the ZWRs reflect the fact that the adiabatic picture is the best zeroth order description in the limit of high fields.