Electron-nuclear correlation in above-threshold double ionization of molecules

We report on the experimental observation of photon energy sharing among two electrons and two ions ejected from a doubly ionized molecule exposed to an intense ultraviolet femtosecond laser pulse. Although two electrons are successively released one after the other, bridged by the nuclear motion via their interactions, photon energy sharing among four particles is observed as multiple energy conservation lines in their joint energy spectrum. For sequential double ionization of H2, the electron-nuclear joint energy spectrum allows us to identify three pathways towards the charge-resonance enhanced ionization of the stretching H2+ in strong laser fields. By counting the photon number absorbed by the molecule, we trace the accessibility, enhancement, and suppression of various pathways. The correlated electron-nuclear motion provides profound insights of the complicated strong-field dynamics of molecules.