Bose-Einstein condensation in exotic geometries

Modern quantum engineering techniques allow the synthesis of quantum systems in exotic geometries, including fractal lattices characterized by a self-similar pattern and fractal dimensions, or hyperbolic lattices characterized by negative curvature. These geometries can significantly modify single and many-body quantum behavior. We focus on the properties of Bose-Einstein condensation in such geometries. Due to long-range coherence, the condensate wave function is sensitive to the structure of the lattice, which manifests itself in the momentum distribution. It is found that, while the fractal geometry leads to a significant suppression of the critical temperature, the hyperbolic lattice strongly favors condensation. Unlike other 2D systems, the critical temperature in a hyperbolic lattice increases with the system size, hinting for a stable 2D condensate in the thermodynamic limit and at finite temperature. The influence of both finite size and boundary effects has to be considered, as the studied geometries possess a nonvanishing fraction of boundary sites even in the thermodynamic limit.