Two types of BCS-BEC crossover of atomic Fermi superfluidin a spherical bubble trap*

Inspired by the spherical bubble traps in microgravity, 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 Ferm gas on a spherical shell, the properly normalized gap and chemical potential of Fermi superfluid exhibit universal behavior regardless of the planar or spherical geometry. By tuning the attractive interaction, an interaction-induced BCS-BEC crossover occurs. However, we consider a different scenario where the particle number and interaction strength are fixed but the sphere is shrinking. The 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, pushing the system towards the BCS limit. The curvature-induced BCS-BEC crossover is made possible by the compact geometry, exemplified by the spherical bubble traps. The theory paves the way for a systematic study of atomic Fermi superfluid in spherical geometry.