We report the observation of dramatic consequences of dimensional reduction onto the motional state of a quantum gas restricted to a curved two-dimensional surface. We start from the ellipsoidal geometry of a dressed quadrupole trap and introduce a novel gravity compensation mechanism enabling to explore the full ellipsoid. The dimensional reduction manifests itself by the spontaneous emergence of an annular shape in the atomic distribution, due to the zero-point energy of the transverse confinement. The experimental results are compared with the solution of the three dimensional Gross-Pitaevskii equation and with a two-dimensional semi-analytical model. This work evidences how a hidden dimension can affect dramatically the embedded low dimensional system by inducing a change of topology.
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