# Exotic states in the strong field control of H$_2^+$ dissociation dynamics: From exceptional points to zero-width resonances

## TL;DR

This paper explores strong field control of H$_2^+$ dissociation, focusing on zero-width resonances and exceptional points, developing a Floquet-based adiabatic theory, and demonstrating selective vibrational control through numerical and wavepacket analyses.

## Contribution

It introduces a Floquet Hamiltonian-based adiabatic transport theory for multiphoton dynamics, highlighting the distinct treatment of ZWRs and EPs in controlling molecular dissociation.

## Key findings

- Full control over vibrational states demonstrated.
- Numerical maps optimize laser parameters for selective control.
- Robust vibrational filtering achieved within experimental constraints.

## Abstract

H$_2^+$ is an ideal candidate for a 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 (ZWR) on one hand, and coalescing pairs of resonances at exceptional points (EP) on the other hand. An adiabatic transport theory based on 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 experimental feasibility criteria.