Shortcuts to adiabaticity by counter-diabatic driving

The evolution of a system induced by counter-diabatic driving mimics the adiabatic dynamics without the requirement of slow driving. Engineering it involves diagonalizing the instantaneous Hamiltonian of the system and results in the need of auxiliary non-local interactions for matter-waves. Here experimentally realizable driving protocols are found for a large class of single-particle, many-body, and non-linear systems without demanding the spectral properties as an input. The method is applied to the fast decompression of Bose-Einstein condensates in different trapping potentials.