  Using numerical simulations of two-photon electronic absorption with
femtosecond pulses in Na$_2$ we show that: i) it is possible to avoid the
characteristic saturation or dumped Rabi oscillations in the yield of
absorption by time-delaying the laser pulses; ii) it is possible to accelerate
the onset of adiabatic passage by using the vibrational coherence starting in a
wave packet; and iii) it is possible to prepare the initial wave packet in
order to achieve full state-selective transitions with broadband pulses. The
findings can be used, for instance, to achieve ultrafast adiabatic passage by
light-induced potentials and understand its intrinsic robustness.
