Excitation Spectra of one-dimensional spin-1/2 Fermi gas with an attraction

TL;DR

This paper uses exact Bethe ansatz methods to analyze the excitation spectra of an attractive one-dimensional spin-1/2 Fermi gas, revealing novel collective modes and providing analytical expressions for low-momentum excitations.

Contribution

It provides the first detailed analytical and numerical characterization of excitation spectra, including particle-hole and magnon excitations, in the attractive Fermi gas with FFLO-like states.

Findings

Analytical expressions for excitation dispersions at small momentum

Identification of separated collective modes of paired and unpaired fermions

Discussion of magnon excitations and experimental testing via Bragg spectroscopy

Abstract

Using exact Bethe ansatz solution, we rigorously study excitation spectra of the spin-1/2 Fermi gas (called Yang-Gaudin model) with an attractive interaction. Elementary excitations of this model involve particle-hole excitations, hole excitations and adding particles in the Fermi seas of pairs and unpaired fermions. The gapped magnon excitations in spin sector show a ferromagnetic coupling to the Fermi sea of the single fermions. By numerically and analytically solving the Bethe ansatz equations and the thermodynamic Bethe ansatz equations of this model, we obtain excitation energies for various polarizations in the phase of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state. For a small momentum (long-wavelength limit) and in the strong interaction regime, we analytically obtained their linear dispersions with curvature corrections, effective masses as well as velocities in particle-hole excitations of pairs and unpaired fermions. Such a type of particle-hole excitations display a novel separation of collective motions of bosonic modes within paired and unpaired fermions. Finally, we also discuss magnon excitations in spin sector and the application of the Bragg spectroscopy for testing such separated charge excitation modes of pairs and single fermions.