  Different techniques to speed up quantum adiabatic processes are currently
being explored for applications in atomic, molecular and optical physics, such
as transport, cooling and expansions, wavepacket splitting, or internal state
control. Here we examine the capabilities of superadiabatic iterations to
produce a sequence of shortcuts to adiabaticity. The general formalism is
worked out as well as examples for population inversion in a two-level system.
