Speaker
Description
Recent experimental realizations of ultracold atom bubble traps in microgravity conditions have triggered the exploration of quantum many-body physics in curved geometries, beyond the flat-space paradigm. We investigate a two-component Fermi gas on a spherical surface, analyzing how the interplay between curvature and interactions modifies its physical properties, both at finite and zero temperatures. Starting from the non-interacting case, we derive the finite-temperature Stoner criterion for repulsive interactions to study the stability of the spin-balanced phase. Furthermore, we explore the BCS–BEC crossover as the system evolves from a weakly paired (BCS) regime to a strongly paired (BEC) regime. Across all the investigated regimes, our results reveal the emergence of pronounced shell effects and curvature-induced corrections that significantly deviate from standard two-dimensional flat-space predictions, especially in the low-temperature regime. Remarkably, while differences with respect to flat case results tend to zero in the deep BEC regime, where the dimers have a size much smaller than the sphere, such differences instead are extremely marked in the deep BCS regime. In this limit, the Cooper pair size is bounded by the sphere radius $R$, forcing the system to probe the global curvature of the manifold.