Cold atoms in gravity and microgravity

最近在ZARM的不莱梅落塔中实现了自由落体过程中玻色-爱因斯坦凝聚体（BEC）的制备和观测。在超过1秒的自由膨胀过程中，原子形成了一个巨大的相干物质波，在毫米尺度上离域。这代表了一个独特的量子系统，可以进行新的实验来测试量子理论及其与引力的耦合，并寻找假设的量子引力效应。因此，在这个项目中，我们（i）希望从理论上讨论研究自由演化和弱引力场中由Gross-Pitaevskii方程（GPE）描述的BEC动力学的可能实验。特别是，我们喜欢计算定态和动力学的BEC在弱均匀和非均匀的引力场，除其他外，形成一个巨大的引力氢原子的可能性。我们还想讨论的影响（ii）的形状的陷阱，小颗粒的数量，并可能修改的色散关系和（iii）一个波动的环境，特别是也是一个波动的度量，对BECs的物理和统计特性。还应研究增强波动影响的可能性。在所有的情况下，我们讨论的可行性进行这样的实验在落塔。

The preparation and observation of a Bose–Einstein condensate (BEC) during free fall has been realized recently in the Bremen drop tower at ZARM. During the free expansion over 1 second, the atoms form a giant coherent matter wave that is delocalized on a millimeter scale. This represents a unique quantum system which allows to perform new experiments for testing quantum theory and its coupling to gravity, and for the search for hypothetical quantum gravity effects. Accordingly, in this project we (i) like to theoretically discuss possible experiments studying the dynamics of BECs, described by the Gross–Pitaevskii equation (GPE), in free evolution and weak gravitational fields. In particular we like to calculate stationary states and the dynamics of a BEC in weak homogeneous and inhomogeneous gravitational fields, among other, the possibility to form a giant gravitational hydrogen atom. We also would like to discuss the effects of (ii) the shape of traps, small particle numbers, and possibly modified dispersion relations and of (iii) a fluctuating environment, in particular also a fluctuating metric, on the thermodynamical and statistical properties of BECs. Also possibilities to enhance the effect of fluctuations shall be investigated. In all cases we discuss the feasibility for such experiments to be carried out in the drop tower.