  We use the dynamical invariants associated with the Hamiltonian of an atom in
a one dimensional moving trap to inverse engineer the trap motion and perform
fast atomic transport without final vibrational heating. The atom is driven
non-adiabatically through a shortcut to the result of adiabatic, slow trap
motion. For harmonic potentials this only requires designing appropriate trap
trajectories, whereas perfect transport in anharmonic traps may be achieved by
applying an extra field to compensate the forces in the rest frame of the trap.
The results can be extended to atom stopping or launching. The limitations due
to geometrical constraints, energies and accelerations involved are analyzed,
as well as the relation to previous approaches (based on classical trajectories
or "fast-forward" and "bang-bang" methods) which can be integrated in the
invariant-based framework.
