  Precise control of quantum particles is required for many interesting or
novel experiments. Here we consider the task of transporting an atom using an
external harmonic potential from one well of an optical lattice to another
without motional excitations. To achieve this we apply techniques from
Shortcuts to Adiabaticity (STA) enabling fast and robust state manipulation.
The process is split up into three independent building blocks; first the atom
is loaded into an additional external harmonic trap; this trap is then
transported from one lattice site to another and finally the atom is unloaded
back onto the lattice by opening the external harmonic trap. We design
protocols for each of these building blocks separately using invariant-based
inverse engineering. Additionally we extend this method to the transport of a
Bose-Einstein condensate described by the Gross-Pitaevskii equation.
