  We study the shuttling of an atom in a trap with controllable position and
frequency. Using invariant-based inverse engineering, protocols in which the
trap is simultaneously displaced and expanded are proposed to speed up
transport between stationary trap locations as well as launching processes with
narrow final-velocity distributions. Depending on the physical constraints
imposed, either simultaneous or sequential approaches may be faster. We
consider first a perfectly harmonic trap, and then extend the treatment to
generic traps. Finally, we apply this general framework to a double-well
potential to separate different motional states with different launching
velocities.
