Coupling constants for a degenerate Fermi gas confined to a quasi one-dimensional harmonic trap

TL;DR

This paper develops a theoretical framework to determine the coupling constants between spin-polarized degenerate fermionic atoms confined in a quasi-one-dimensional harmonic trap, highlighting the dominance of backscattering in identical fermions.

Contribution

It introduces a parameterization of effective one-dimensional interactions with three sets of coefficients, including analytic expressions for contact and p-wave interactions, and applies this to dipole-dipole interactions.

Findings

Effective interaction characterized by three sets of coefficients.

Backscattering dominates for identical fermions.

Analytic expressions derived for contact and p-wave interactions.

Abstract

A theory for the coupling constants between spin polarized degenerate fermionic atoms is developed for the case of atoms confined to a quasi one-dimensional harmonic trap. Exploiting the presence of the Fermi edge and the large number of fermions it is shown that the resulting effective one-dimensional interaction can be parameterized by three sets of interaction coefficients, two for forward scattering and one for backward scattering. In the case of identical fermions, backscattering dominates because the contact part of the effective one-dimensional interaction must be subtracted. Analytic expressions for the interaction coefficients for the effective contact interaction, which is relevant for the inter-component interactions, and for the "p-wave" interaction appearing in next order, are given. As an example, we calculate and discuss in detail the effective coupling constants for the marginally long ranged dipole--dipole interaction.