Shortcuts to adiabaticity for ultracold gases

In order to manipulate Bose?Einstein condensates for different applications, it is important to study and control their response to time-dependent changes of the confining fields. A natural approach to avoid undesired excitations is to modify the trap adiabatically, i.e. very slowly, so that, if the initial state is in the ground state the final state will be the ground state as well. However, this may require very long times and become impractical. Thus natural objective is to cut down the time to arrive at the same final state, in other words, to find shortcuts to adiabaticity, by designing optimal adiabatic pathways.In this thesis, fast frictionless expansion for growing Bose?Einstein condensates described by the Gross?Pitaevskii gain equation is investigated. It is shown that fast frictionless expansion can be generalized to a condensate continuously replenished by pumping from the reservoir. Our formalism is applied to the harmonically trapped condensate and an optical lattice.Key Words: Bose?Einstein condensates, harmonically trapped condensate, an optical lattice, shortcuts to adiabaticity.