Realization of effective super Tonks-Girardeau gases via strongly attractive one-dimensional Fermi gases

TL;DR

This paper demonstrates that strongly attractive one-dimensional Fermi gases can be effectively realized as super Tonks-Girardeau gases of bosonic pairs, exhibiting unique statistical properties and metastable behavior.

Contribution

It introduces a novel effective description of strongly attractive Fermi gases as super Tonks-Girardeau gases of bosonic pairs using generalized exclusion statistics.

Findings

Super Tonks-Girardeau gases exhibit stronger Fermi-like pressure preventing collapse.

Effective bosonic pair description captures metastable behavior of attractive Fermi gases.

Particles obey more exclusive statistics than Fermi-Dirac, as described by Haldane statistics.

Abstract

A significant feature of the one-dimensional super Tonks-Girardeau gas is its metastable gas-like state with a stronger Fermi-like pressure than for free fermions which prevents a collapse of atoms. This naturally suggests a way to search for such strongly correlated behaviour in systems of interacting fermions in one dimension. We thus show that the strongly attractive Fermi gas without polarization can be effectively described by a super Tonks-Girardeau gas composed of bosonic Fermi pairs with attractive pair-pair interaction. A natural description of such super Tonks-Girardeau gases is provided by Haldane generalized exclusion statistics. In particular, we find that they are equivalent to ideal particles obeying more exclusive statistics than Fermi-Dirac statistics.