We perform high-resolution measurements of momentum distribution on Rb$^{n+}$ recoil ions up to charge state $n=4$, where laser-cooled rubidium atoms are ionized by femtosecond elliptically polarized lasers with the pulse duration of 35 fs and the intensity of 3.3$times$10$^{15}$ W/cm$^2$ in the over-barrier ionization (OBI) regime. The momentum distributions of the recoil ions are found to exhibit multi-band structures as the ellipticity varies from the linear to circular polarizations. The origin of these band structures can be explained quantitatively by the classical OBI model and dedicated classical trajectory Monte Carlo simulations with Heisenberg potential. Specifically, with back analysis of the classical trajectories, we reveal the ionization time and the OBI geometry of the sequentially released electrons, disentangling the mechanisms behind the tilted angle of the band structures. These results indicate that the classical treatment can describe the strong-field multiple ionization processes of alkali atoms.
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