Optimal quantum control of trapped Bose-Einstein condensates

Magnetic microtraps on atom chips enable precise and robust quantum control of Bose-Einstein condensates (BECs). These are macroscopic quantum objects which are very well isolated from the environment. A key application is an atom interferometer built with trapped BECs. The major goal of this thesis is the optimal quantum control of trapped BECs for atom interferometry applications, as well as a better understanding of the involved physical processes. For control purposes and for non-adiabatic condensate dynamics, elaborate time dependent methods are necessary. We use the Multi-configurational time-dependent Hartree for Bosons (MCTDHB) method, which provides a hierarchy of efficient approximation schemes. Realization of atom interferometers will require elaborate control strategies. We implement thus Optimal control theory for MCTDHB and apply it to several problems. One application is number squeezing by splitting of BECs, which we achieve one order of magnitude faster as compared to quasi-adiabatic splitting. The rapid condensate dynamics resulting from our OCT protocols poses the general question about condensate excitations and stability of the condensate during splitting. Simulations with more than two modes allow us to obtain insight into the many-body dynamics. We analyse trapped BEC interferometers in presence of interactions, in particular the optimal input states and how they can be prepared using quantum control. We find that the MZ interferometer is particularly promising, if Bayesian phase estimation is used. We conclude that phase diffusion is not a substantial limitation for atom interferometry, which could have significant impact on the realization of atom interferometers. (author)