Shortcuts to adiabaticity in the double well

Shortcuts to adiabaticity are alternative fast processes that reproduce the same final populations, or even the same final state, as the adiabatic process in a finite, shorter time. Many of the existing approaches to design shortcuts, and even new ones have been used throughout this Thesis in the double well potential. These techniques have allowed us to obtain a great benefit in processes as varied as matter-wave splitting, multiplexing/ demultiplexing, beam splitters, cotunneling, population inversion, waveguide optimization, Tonks-Girardeau gas manipulation and bias inversion.