Visualizing electron delocalization, electron-proton correlations, and the Einstein-Podolsky-Rosen paradox during the photodissociation of a diatomic molecule using two ultrashort laser pulses

We investigate theoretically the dissociative ionization of an H₂⁺ molecule using two ultrashort laser (pump-probe) pulses. The pump pulse prepares a dissociating nuclear wave packet on an ungerade surface of H₂⁺. Next, an ultraviolet [or extreme ultraviolet (XUV)] probe pulse ionizes this dissociating state at large ($R=20--100$ bohr) internuclear distance. We calculate the momenta distributions of protons and photoelectrons which show a (two-slit-like) interference structure. A general, simple interference formula is obtained which depends on the electron and protons momenta, as well as, on the pump-probe delay and also on the durations and polarizations of the laser pulses. This pump-probe scheme reveals a striking quantum delocalization of the electron over two protons which intuitively should be localized on just one of the protons separated by the distance R much larger than the atomic Bohr orbit.