  In the previous paper on this topic it was shown how, for a pulse of
arbitrary shape and duration, the drive frequency can be analytically optimized
to maximize the amplitude of the population oscillations between the selected
two levels in a general many level quantum system. It was shown how the
standard Rabi theory can be extended beyond the simple two-level systems. Now,
in order to achieve the quickest and as complete as possible population
transfer between two pre-selected levels, driving pulse should be tailored so
that it produces only a single half-oscillation of the population. In this
paper, this second (and final) step towards the controlled population transfer
using modified (i.e. many level system) Rabi oscillations is discussed. The
results presented herein can be regarded as an extension of the standard
$\pi$-pulse theory - also strictly valid only in the two level systems - to the
coherently driven population oscillations in general many level systems.
