Stability of spinor Fermi gases in tight waveguides

TL;DR

This paper investigates the stability of ultracold spin-1/2 Fermi gases in one-dimensional waveguides, revealing conditions under which they are stable against three-body recombination, and analyzing the effects of various interactions.

Contribution

It provides an exact mapping of the spinor Fermi gas to a Lieb-Liniger-Heisenberg model and identifies stable regions in the coupling constant plane, including effects of dipolar and Zeeman interactions.

Findings

SFG is stable against three-body recombination in a large coupling region.

The fermionic Tonks-Girardeau gas is unstable under these conditions.

Dipolar and Zeeman interactions do not significantly alter the stability region.

Abstract

The two and three-body correlation functions of the ground state of an optically trapped ultracold spin-1/2 Fermi gas (SFG) in a tight waveguide (1D regime) are calculated in the plane of even and odd-wave coupling constants, assuming a 1D attractive zero-range odd-wave interaction induced by a 3D p-wave Feshbach resonance, as well as the usual repulsive zero-range even-wave interaction stemming from 3D s-wave scattering. The calculations are based on the exact mapping from the SFG to a ``Lieb-Liniger-Heisenberg'' model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, and indicate that the SFG should be stable against three-body recombination in a large region of the coupling constant plane encompassing parts of both the ferromagnetic and antiferromagnetic phases. However, the limiting case of the fermionic Tonks-Girardeau gas (FTG), a spin-aligned 1D Fermi gas with infinitely attractive p-wave interactions, is unstable in this sense. Effects due to the dipolar interaction and a Zeeman term due to a resonance-generating magnetic field do not lead to shrinkage of the region of stability of the SFG.