Semiclassical limit Bose-Einstein condensate dynamics

超冷玻色气体已被证明是物理学许多不同方面的理想实验测试平台。此外，在设计的时空相关势中对弱相互作用玻色气体的理论描述是非常具有挑战性的。在这个建议中，我们希望在理论和实验之间密切合作的情况下遵循这两条路线。在实验部分，我们将利用超冷气体探索新的有效的预测制度，特别是半经典的限制似乎是第一次访问。作为第一个例子之一，我们将探讨实现单粒子经典哈密顿棘轮的可能性，采用灵活的设计的时间和空间的潜力和强大的本地化相空间由于非常低的温度。与迄今为止进行的实验相比，新系统允许实现具有长波长的驱动周期电位，从而导致小的有效预测值。量子气体系统也允许以不同的方式探索半经典极限，通过将平均场处理确定为完整量子力学多体描述的经典对应物。在这种情况下，有效的预测与粒子数成反比，粒子数可以通过实验在几个数量级上改变，从而提供独特的系统。具体来说，我们将探讨驱动动力学的玻色-爱因斯坦凝聚体在双和多阱系统，其中平均场以及某些许多粒子方面的实验是可以访问的。从理论上讲，我们将开发不同的有效的描述，将测试对实验结果，但也相应的几个粒子问题的精确解。

Ultracold Bose gases have proven to be an ideal experimental test bed for many different aspects of physics. Furthermore the theoretical description of weakly interacting Bose gases in designed time-spatial dependent potentials is very challenging. In this proposal we want to follow both routes in close collaboration between theory and experiment. In the experimental part we will utilize ultracold gases for the exploration of new effective ħ regimes where especially the semiclassical limit seems for the first time accessible. As one of the first examples we will explore the possibilities of the realization of a single particle classical Hamiltonian ratchet, employing the flexible design of temporal and spatial potentials and the strong localization in phase space due to the very low temperature. In contrast to the experiments performed so far the new systems allows the realization of driven periodic potentials with long wavelengths leading to small effective ħ values. The quantum gas system also allows the exploration of the semiclassical limit in a different way, by identifying the meanfield treatment as the classical counterpart to the full quantum mechanical many body description. In this context the effective ħ scales inversely with the particle number which can be changed experimentally over few orders of magnitude offering a unique system. Specifically we will explore driven dynamics of Bose-Einstein condensates in double and many well systems, where meanfield as well as certain many particle aspects are accessible experimentally. Theoretically we will develop different effective descriptions which will be tested against experimental results but also to exact solutions of the corresponding few particle problem.