Low-dimensional quantum gases in curved geometries

Atomic gases confined in curved geometries are characterized by distinctive features that are absent in their flat counterparts, such as periodic boundaries, local curvature, and nontrivial topologies. The recent experiments with shell-shaped quantum gases and the study of ring-shaped superfluids point out that the manifold of a quantum gas could soon become a controllable feature, thus allowing to address the fundamental study of curved many-body quantum systems. Here, we review the main geometries realized in the experiments, analyzing the theoretical and experimental status on their phase transitions and on the superfluid dynamics. In perspective, we delineate the study of vortices, the few-body physics, and the search for analog models in various curved geometries as the most promising research areas.