Dynamics of Bose-Einstein Condensates

该提案是对非线性结构的相位工程工作的延续，以及气态原子玻色-爱因斯坦凝聚体（BEC）中的高度纠缠数态，以及由此产生的工作提案，在检测这种纠缠态的实际情况中，以及量子宏观叠加态的相对相位的测量。此外，PI正在开发一种组合计算理论，该理论包括“完整”平均场效应，通过耦合GP（Gross-Piteavskii）方程的解，同时完整（或近似用于两个以上阱）处理相关性，以便正确保持分裂“凝聚体之间的相位关系，并且可以描述海森堡有限测量所需的相干和纠缠态。正确处理相关性和平均场效应是计算和智力密集型的，但对于模拟当前的实验以及对冷凝行为进行现实的预测是必要的。

The proposal is a continuation of work on phase engineering of non-linear structures, and highly entangled number states in gaseous atomic Bose-Einstein condensates, or BECs, and proposals for work, growing out of this, in the actualities of detection of such entangled states, and the masurement of the relative phase of quantum macroscopic superposition states. In addition, the PI is developing a combined computational theory which includes "full" mean field effects, through solution of coupled GP (Gross-Piteavskii) equations, and simultaneously full (or approximate for more than two well traps) treatment of correlations, so that phase relations between split" condensates are properly maintained, and the coherent and entangled states needed for Heisenberg limited measurements can be described. Correct treatment of both correlation and mean-field effects is computationally and intellectually intensive, but necessary for modeling current experiments, as well as making realistic predictions of condensate behavior.