Excitation spectrum and effective interactions of highly-elongated Fermi gas

TL;DR

This paper performs detailed 3D and 1D calculations on highly-elongated two-component Fermi gases to understand their excitation spectra and effective interactions, validating simplified models for small systems.

Contribution

It compares full 3D and effective 1D models to establish their validity regimes and derives analytical expressions for effective interactions in small Fermi systems.

Findings

Effective 1D models accurately describe small Fermi gases within certain regimes.

Analytical expressions for atom-dimer and dimer-dimer interactions are validated.

Comparison of energies and excitation frequencies supports the use of simplified models.

Abstract

Full 3D calculations of small two-component Fermi gases under highly-elongated confinement, in which unlike fermions interact through short-range potentials with variable atom-atom s-wave scattering length, are performed using the correlated Gaussian approach. In addition, microscopic 1D calculations are performed for effective "atomic" and "molecular" 1D model Hamiltonian. Comparisons of the 3D and 1D energies and excitation frequencies establish the validity regimes of the effective 1D Hamiltonian. Our numerical results for three- and four-particle systems suggest that the effective 1D atom-dimer and dimer-dimer interactions are to a good approximation determined by simple analytical expressions. Implications for the description of quasi-1D Fermi gases within strict 1D frameworks are discussed.