Optimizing number squeezing when splitting a mesoscopic condensate

Full text: An atom interferometer can be built using Bose Einstein condensates, confined in magnetic traps, which are split by continuously transforming the trapping potential. In order to minimize phase diffusion, due to the nonlinearity originating from atom-atom interactions in the condensate, number squeezing of the atoms in the wells is required. Squeezing occurs when tunneling becomes small due to the nonlinear interaction which favors a sharp number distribution in each well. In adiabatic scenarios, squeezing is severely limited by the timescales of the tunneling dynamics, and therefore non-adiabatic strategies are favorable. In this contribution we show that optimal control theory (OCT) allows to devise control strategies which significantly outperform adiabatic schemes. We first discuss number squeezing in the framework of a generic two-mode model, and give an intuitive physical explanation for the OCT control strategy. For realistic magnetic microtraps, it becomes important to include a non-adiabatic wave function evolution beyond the generic two-mode model. In this work we describe the dynamical evolution of the two orbitals occupied by the atoms within the MCTDHB equations, which are based on a variational principle. Our results cover several squeezing time scales as well as different numbers of atoms in the condensate. We compare adiabatic to non-adiabatic splitting with simple control and optimal control. By using OCT, we can handle non-adiabatic wave function evolution, and obtain number squeezed states on much shorter time scales in comparison to other strategies. (author)