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

TL;DR

This paper develops a theoretical framework for a two-component atomic Fermi gas on a spherical shell, exploring how curvature and interaction tuning induce the BCS-BEC crossover, with universal behavior observed across geometries.

Contribution

It introduces a curvature-induced BCS-BEC crossover mechanism in spherical geometries, extending the understanding of superfluid behavior in curved quantum systems.

Findings

Universal behavior of gap and chemical potential across geometries

Curvature can induce BCS-BEC crossover by shrinking the sphere

Superfluid density saturation confirms Fermi superfluid ground state

Abstract

We present a theory of a two-component atomic Fermi gas with tunable attractive contact interactions on a spherical shell going through the Bardeen-Cooper-Schrieffer (BCS) - Bose Einstein condensation (BEC) crossover, inspired by the realizations of spherical bubble traps for ultracold atoms in microgravity. The derivation follows the BCS-Leggett theory to obtain the gap and number equations. The BCS-BEC crossover can be induced by tuning the interaction, and the properly normalized gap and chemical potential exhibit universal behavior regardless of the planar or spherical geometry. Nevertheless, the spherical-shell geometry introduces another way of inducing the crossover by the curvature. The curvature-induced BCS-BEC crossover is made possible by fixing the particle number and interaction strength while shrinking the sphere, causing a reduction to the ratio of the pairing and kinetic energies and pushing the system towards the BCS limit. The saturation of the superfluid density further confirms the ground state is a Fermi superfluid.