Fast optimal transition between two equilibrium states

We demonstrate a technique based on invariants of motion for a time-dependent Hamiltonian, allowing a fast transition to a final state identical in theory to that obtained through a perfectly adiabatic transformation. This method is experimentally applied to the fast decompression of an ultracold cloud of ⁸⁷Rb atoms held in a harmonic magnetic trap in the presence of gravity. We are able to decompress the trap by a factor of $15$ within $35$ ms with a strong suppression of the sloshing and breathing modes induced by the large vertical displacement and curvature reduction of the trap. When compared to a standard linear decompression, we achieve a gain of a factor of $37$ on the transition time.