  We work out the theory and applications of a fast quasi-adiabatic approach to
speed up slow adiabatic manipulations of quantum systems by driving a control
parameter as near to the adiabatic limit as possible over the entire protocol
duration. Specifically, we show that the population inversion in a two-level
system, the splitting and cotunneling of two-interacting bosons, and the
stirring of a Tonks-Girardeau gas on a ring to achieve mesoscopic
superpositions of many-body rotating and non-rotating states, can be
significantly speeded up.
