Swallowtail Band Structure of the Superfluid Fermi Gas in an Optical Lattice

TL;DR

This paper explores the band structure of superfluid Fermi gases in optical lattices, revealing swallowtail formations near unitarity and their effects on quasiparticle spectra and incompressibility across the BCS-BEC crossover.

Contribution

It demonstrates the emergence of swallowtail structures in the energy bands of superfluid Fermi gases and analyzes their dependence on interaction strength across the BCS-BEC crossover.

Findings

Swallowtail structures appear above a critical interaction strength.

Largest swallowtail width occurs near unitarity.

Incompressibility dips sharply on the BCS side near the swallowtail.

Abstract

We investigate the energy band structure of the superfluid flow of ultracold dilute Fermi gases in a one-dimensional optical lattice along the BCS to BEC crossover within a mean-field approach. In each side of the crossover region, a loop structure (swallowtail) appears in the Bloch energy band of the superfluid above a critical value of the interaction strength. The width of the swallowtail is largest near unitarity. Across the critical value of the interaction strength, the profiles of density and pairing field change more drastically in the BCS side than in the BEC side. It is found that along with the appearance of the swallowtail, there exists a narrow band in the quasiparticle energy spectrum close to the chemical potential and the incompressibility of the Fermi gas consequently experiences a profound dip in the BCS side, unlike in the BEC side.