  When a molecule is exposed to a laser field, all field-free vibrational
states become resonances, with complex quasi energies calculated using Floquet
theory. There are many ways to produce the coalescences of pairs of such quasi
energies, with appropriate wavelength-intensity choices which define
Exceptional Points (EP) in the laser parameter plane. We dress for the
molecular ion H$_2^+$ an exhaustive map of these exceptional points which
appear in clusters. Such clusters can be used to define several vibrational
transfer scenarios implying more than a single exceptional point, exchanging
single or multiple vibrational quanta. The ultimate goal is molecular
vibrational cooling by transferring an initial (thermal, for instance)
population on a final (ground, for instance) single vibrational state. When a
molecule is exposed to a laser field, all field-free vibrational states become
resonances, with complex quasi energies calculated using Floquet theory. There
are many ways to produce the coalescences of pairs of such quasi energies, with
appropriate wavelength-intensity choices which define Exceptional Points (EP)
in the laser parameter plane. We dress for the molecular ion H$_2^+$ an
exhaustive map of these exceptional points which appear in clusters. Such
clusters can be used to define several vibrational transfer scenarios implying
more than a single exceptional point, exchanging single or multiple vibrational
quanta. The ultimate goal is molecular vibrational cooling by transferring an
initial (thermal, for instance) population on a final (ground, for instance)
single vibrational state.
