Tonks-Girardeau and Super Tonks-Girardeau States of a Trapped 1D Spinor Bose Gas

TL;DR

This paper investigates the exact ground and excited states of a 1D spin-1 Bose gas under strong interactions, revealing the stability of hybrid TG states and proposing experimental creation methods for super Tonks-Girardeau states.

Contribution

It introduces a new exact hybrid TG state in a 1D spinor Bose gas and explores its stability and experimental realization under sudden interaction switches.

Findings

Hybrid TG state remains stable under infinite attraction.

Metastable super TG states can be created by sudden interaction switches.

Bound dimer STG states are unlikely to be experimentally realized via interaction switching.

Abstract

A harmonically trapped ultracold 1D spin-1 Bose gas with strongly repulsive or attractive 1D even-wave interactions induced by a 3D Feshbach resonance is studied. The exact ground state, a hybrid of Tonks-Girardeau (TG) and ideal Fermi gases, is constructed in the TG limit of infinite even-wave repulsion by a spinor Fermi-Bose mapping to a spinless ideal Fermi gas. It is then shown that in the limit of infinite even-wave attraction this same state remains an exact many-body eigenstate, now highly excited relative to the collapsed generalized McGuire cluster ground state, showing that the hybrid TG state is completely stable against collapse to this cluster ground state under a sudden switch from infinite repulsion to infinite attraction. It is shown to be the TG limit of a hybrid super Tonks-Girardeau (STG) state which is metastable under a sudden switch from finite but very strong repulsion to finite but very strong attraction. It should be possible to create it experimentally by a sudden switch from strongly repulsive to strongly attractive interaction, as in the recent Innsbruck experiment on a spin-polarized bosonic STG gas. In the case of strong attraction there should also exist another STG state of much lower energy, consisting of strongly bound dimers, a bosonic analog of a recently predicted STG gas which is an ultracold gas of strongly bound bosonic dimers of fermionic atoms, but it is shown that this STG state cannot be created by such a switch from strong repulsion to strong attraction.