Exact non-Born-Oppenheimer numerical solutions of the time-dependent Schr\odinger equation for the one-dimensional ${\mathrm{H}}_{2}^{+}$ molecule in an intense, two-color $(\ensuremath{\omega}+2\ensuremath{\omega})$ laser field, with relative phase $\ensuremath{\varphi},$ have been obtained. Both electron and proton kinetic energy spectra show spatial, correlated, asymmetric distributions. The calculated spectra exhibit the same unusual correlations as seen in experiments, in which both positively charged nuclear fragments and negatively charged photoelectrons are preferentially emitted in the same direction. It is found that, for the most asymmetric combined electric field $(\ensuremath{\varphi}=0),$ the electron is ionized in a ``counterintuitive'' direction: i.e., more electrons follow the direction of the maximum electric field. This unexpected behavior of electrons is not specific to molecules: we show that the same effect occurs in atoms. The above asymmetries of photoemission of electrons are interpreted in the framework of a quasistatic tunneling model and it is shown that for $\ensuremath{\varphi}=0$ the electron asymmetry is induced by the Coulomb attraction from the parent ion. Proton asymmetries found in the dissociation $\mathrm{H}+p$ channel depend strongly on the initialization: proton asymmetry for low vibrational state initialization is opposite that for high vibrational states. In the latter case, for $\ensuremath{\varphi}=0,$ protons follow the direction of the maximum field. Coulomb explosion spectra are shown to arise from an enhanced ionization mechanism, which is phase dependent also.
Read full abstract