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We design optimal harmonic-trap trajectories to transport cold atoms withoutfinal excitation, combining an inverse engineering techniqe based onLewis-Riesenfeld invariants with optimal control theory. Since actual traps arenot really harmonic, we keep the relative displacement between the center ofmass and the trap center bounded. Under this constraint, optimal protocols arefound according to different physical criteria. The minimum time solution has a"bang-bang" form, and the minimum displacement solution is of "bang-off-bang"form. The optimal trajectories for minimizing the transient energy are alsodiscussed.

Optimal trajectories for efficient atomic transport without final excitation