Cold atoms in gravity and microgravity

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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.