In the framework of a basic semiclassical time-dependent nonlinear two-state problem, we study the weak coupling limit of the nonlinear Landau-Zener transition at coherent photo- and magneto-association of an atomic Bose-Einstein condensate. Using an exact third-order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct an accurate analytic approximation describing time dynamics of the coupled atom-molecular system for the case of weak coupling. The approximation is written in terms of the solution to an auxiliary linear Landau-Zener problem with some effective Landau-Zener parameter. The dependence of this effective parameter on the input Landau-Zener parameter is found to be unexpected: as the generic Landau-Zener parameter increases, the effective Landau-Zener parameter first monotonically increases (starting from zero), reaches its maximal value and then monotonically decreases again reaching zero at some point. The constructed approximation quantitatively well describes many characteristics of the time dynamics of the system, in particular, it provides a highly accurate formula for the final transition probability to the molecular state. The present result for the final transition probability improves the accuracy of the previous approximation by Ishkhanyan et al. [Phys. Rev. A 69, 043612 (2004); J. Phys. A 38, 3505 (2005)] by order of magnitude.
Many-body Landau-Zener dynamics in coupled 1D Bose liquids
量子力学的朗道-齐纳模型的两个能级系统驱动的线性时间依赖的失谐已经作为量子动力学的教科书范例了几十年。在他们的开创性工作[L。D.朗道，物理学。Z.索杰特2，46（1932）; C. Zener，Proc. Royal Soc. London 137，696（1932）]，Landau和Zener导出了两个状态之间的跃迁概率的非微扰预测，其通常用作分析更复杂系统的参考点。一个特别有趣的问题是，这个框架是否可以扩展到描述多体量子动力学。在这里，我们报告的超冷原子系统的实验和理论研究，提供了一个直接的多体推广的朗道-齐纳问题。在成对的隧道耦合的一维玻色液体的系统中，我们展示了如何调整的相关性的一维气体，隧道之间的耦合管和管间的相互作用强烈修改原来的朗道-齐纳图片。使用平均场描述的管间凝聚波函数，耦合到低能量声子的1D玻色液体的结果进行解释。
