Exotic states in the strong-field control of H-2(+) dissociation dynamics: from exceptional points to zero-width resonances

H-2(+) is an ideal candidate for the detailed study of strong-field coherent control strategies inspired by basic mechanisms referring to some specific photodissociation resonances. Two of them are considered in this work, namely: zero-width resonances (ZWRs) and coalescing pairs of resonances at exceptional points (EPs). An adiabatic transport theory based on the Floquet Hamiltonian formalism is developed within the challenging context of multiphoton dynamics involving nuclear continua. It is shown that a rigorous treatment is only possible for ZWRs, whereas adiabatic transport mediated by EPs is subjected to restrictions. Numerical maps of resonance widths and non-adiabatic couplings in the laser parameter plane help in optimally shaping control pulses. Full time-dependent wavepacket dynamics shows the possibility of selective, robust filtration and vibrational population transfers, within experimentally feasible criteria.