We theoretically analyze atom interferometry based on trapped ultracold atoms, and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is transformed from a single to a double well, which allows to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) can be obtained by optimized splitting protocols. Two types of solutions are found: in the Josephson regime we find an oscillatory tunnel control and a parametric amplification of number squeezing, while in the Fock regime squeezing is obtained solely due to the nonlinear coupling, which is transformed to number squeezing by peaked tunnel pulses. We study splitting and squeezing within the frameworks of a generic two-mode model, which allows us to study the basic physical mechanisms, and the multi-configurational time dependent Hartree for bosons method, which allows for a microscopic modeling of the splitting dynamics in realistic experiments. Both models give similar results, thus highlighting the general nature of these two solution schemes. We finally analyze our results in the context of atom interferometry.
在平均场论近似下，研究了囚禁相互作用原子玻色气体的有效尺寸随温度的变化。在Wang { \it et al.}的早期实验中观察到的平均长度的突然收缩[下巴。Phys. Lett. { \bf 20}，799（2003）]显示出对于玻色-爱因斯坦凝聚（BEC）的良好指示。我们的研究还支持使用的平均宽度的被困玻色气体的无损校准其温度。
