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We study the formation of highly excited neutral atoms during the break-up ofstrongly-driven molecules. Past work on this significant phenomenon has shownthat during the formation of highly excited neutral atoms ($\mathrm{H^{*}}$)during the break-up of H$_{2}$ in a linear laser field the electron thatescapes does so either very quickly or after remaining bound for a few periodsof the laser field. Here, we address the electron-nuclear dynamics in$\mathrm{H^{*}}$ formation in elliptical laser fields, through Coulombexplosion. We show that with increasing ellipticity two-electron effects areeffectively "switched-off". We perform these studies using a toolkit we havedeveloped for semiclassical computations for strongly-driven multi-centermolecules. This toolkit includes the formulation of the probabilities ofstrong-field phenomena in a transparent way. This allows us to identify theshortcomings of currently used initial phase space distributions for theelectronic degrees of freedom. In addition, it includes a 3-dimensional methodfor time-propagation that fully accounts for the Coulomb singularity. Thistechnique has been previously developed in the context of celestial mechanicsand we currently adopt it to strongly-driven systems. Moreover, we allow fortunneling during the time-propagation. We find that this is necessary in orderto accurately describe the fragmentation of strongly-driven molecules.

A toolkit for semiclassical computations for strongly-driven molecules: "frustrated" ionization of H$_{2}$ driven by elliptical laser fields