Two super Tonks-Girardeau states of a trapped 1D spinor Fermi gas

TL;DR

This paper explores two metastable super Tonks-Girardeau states in a trapped 1D spinor Fermi gas with strong attractive interactions, revealing their properties, potential experimental realization, and stability against collapse.

Contribution

It introduces and characterizes two distinct super Tonks-Girardeau states in a 1D spinor Fermi gas with strong attraction, connecting them to known states and analyzing their stability.

Findings

Two metastable super Tonks-Girardeau states identified.

One state is a hybrid of sTG gas and ideal Fermi gas.

Transition probability from ground state to dimer state is very low.

Abstract

A harmonically trapped ultracold 1D spinor Fermi gas with a strongly attractive 1D even-wave interaction induced by a 3D Feshbach resonance is studied. It is shown that it has two different super Tonks-Girardeau (sTG) energy eigenstates which are metastable against collapse in spite of the strong attraction, due to their close connection with 1D hard sphere Bose gases which are highly excited gas-like states. One of these sTG states is a hybrid between an sTG gas with strong $(\uparrow\downarrow$ attractions and an ideal Fermi gas with no $(\uparrow\uparrow)$ or $(\downarrow\downarrow)$ interactions, the sTG component being an exact analog of the recently observed sTG state of a 1D ultracold Bose gas. It should be possible to create it experimentally by a sudden switch of the $(\uparrow\downarrow)$ interaction from strongly repulsive to strongly attractive, as in the recent Innsbruck experiment on the bosonic sTG gas. The other is a trapped analog of a recently predicted sTG state which is an ultracold gas of strongly bound $(\uparrow\downarrow)$ fermion dimers which behave as bosons with a strongly attractive boson-boson interaction leading to sTG behavior. It is proved that the probability of a transition from the ground state for strongly repulsive interaction to this dimer state under a sudden switch from strongly repulsive to strongly attractive interaction is $\ll 1$, contrary to a previous suggestion.