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

Abstract

The structures of multiply quantized vortices (MQVs) of equal-population atomic Fermi superfluid in a rotating spherical bubble trap are analyzed by solving the Bogoliubov-de Gennes (BdG) equation throughout the BCS-Bose Einstein condensation (BEC) crossover. Consistent with the Poincare-Hopf theorem, a pair of vortices emerge at the poles of the rotation axis in the presence of azimuthal symmetry, and the compact geometry provides confinement for the MQVs. While the single-vorticity vortex structure is similar to that in a planar geometry, higher-vorticity vortices exhibit interesting phenomena at the vortex center, such as a density peak due to accumulation of normal Fermi gas and reversed circulation of current due to in-gap states carrying angular momentum, in the BCS regime but not the BEC regime because of the subtle relations between the order parameter and density. The energy spectrum shows the number of the in-gap state branches corresponds to the vorticity of a vortex, and an explanation based on topological correspondence is provided.

Winding real and order-parameter spaces via lump solitons of spinor BEC on sphere

“…While the kinetic energy is typically negligible when compared to the interaction energy in bosonic systems, the Fermi energy of fermions may remain competitive in the presence of interactions [34]. A curvature-induced BCS-BEC crossover on a spherical shell due to the competition of the kinetic and interaction energies has been discussed [52]. Whether the lumps can survive in fermionic systems is an intriguing question.…”

Winding real and order-parameter spaces via lump solitons of spinor BEC on sphere

“…While the kinetic energy is typically negligible when compared to the interaction energy in bosonic systems, the Fermi energy of fermions may remain competitive in the presence of interactions [34]. A curvature-induced BCS-BEC crossover on a spherical shell due to the competition of the kinetic and interaction energies has been discussed [53]. Whether the lumps can survive in fermionic systems is an intriguing question.…”

Large Angular Momentum States in a Graphene Film

“…In this Appendix, details of the determination of the radial line of the spin-down wave function R 2 (ρ) are given. Once that the expression for the spin up R 1 (ρ) has been derived, from the second part of Equation ( 16), one can see that R 2 (ρ) can be obtained through the derivative of the spin-up wave function R 1 (ρ) that is the linear combination of the two CHFs as given in Equations ( 29) and (30).…”

“…Therefore, the comprehension of the behaviour of carbon-based material as C 60 molecules, quantum rings and annuli acted upon by static or dynamic electromagnetic fields is of paramount importance. Far from being of hindrance to the theoretical approach, the quite large size of these molecules may create symmetries which, judiciously exploited, produce deep simplification in the theoretical approach to the problem and often leads to analytical solutions or crucial insight into the physics of the problem [30].…”