  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.
