Curvature-induced BCS-BEC crossover of atomic Fermi superfluid in a spherical bubble trap

The spherical bubble traps in microgravity allows cold atoms to be confined on a spherical surface. By considering a two-component Fermi gas with attractive interactions, we derive and analyze the BCS-Leggett theory of atomic Fermi superfluid on a thin spherical shell. Despite the flat dispersion within each angular momentum number and jumps between adjacent levels of an ideal Fermi gas on a spherical shell, the properly normalized gap and chemical potential of Fermi superfluid exhibit universal behavior regardless of the geometries. The conventional BCS-BEC crossover induced by increasing the interactions occurs on a sphere. However, a curvature-induced BCS-BEC crossover emerges when the particle number and interaction strength are fixed but the sphere is shrinking. Different from a 3D Fermi superfluid, the pairing energy scale of a 2D Fermi superfluid is determined by the two-body binding energy. When placed on a 2D compact geometry like the spherical shell, an increase of the curvature leads to an increase of the Fermi energy and causes a reduction of the ratio between the pairing and kinetic energies. Therefore, the system is pushed towards the BCS limit as the sphere shrinks. The curvature-induced BCS-BEC crossover thus demonstrates the effects of compact geometries in low dimensions on many-body systems.