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
Rubidium 87 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.Comment: 5 pages, 4 figures, an error in Eq. (2) has been correcte