Cold atoms in gravity and microgravity

自由落体过程中玻色-爱因斯坦凝聚体(BEC)的制备和观测最近在ZARM的不来梅落塔中实现。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，该波在毫米尺度上被离域。这代表了一种独特的量子系统，它允许进行新的实验，以测试量子理论及其与引力的耦合，并搜索假设的量子引力效应。因此，在这个项目中，我们(I)希望从理论上讨论在自由演化和弱引力场中研究由Gross-Pitaevskii方程(GPE)描述的BECs动力学的可能的实验。特别是，我们喜欢计算BEC在弱均匀和非均匀引力场中的定态和动力学，以及形成巨型引力氢原子的可能性。我们还想讨论(Ii)陷阱的形状、小粒子数、可能修改的色散关系以及(Iii)起伏环境，特别是起伏度规对BEC热力学和统计性质的影响。还应调查增强波动影响的可能性。在所有情况下，我们都讨论了在落塔中进行这类实验的可行性。

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.