Clusters of Exceptional Points for a Laser Control of Selective Vibrational Transfer

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.