Evidence for the super Tonks-Girardeau gas

We provide evidence in support of a recent proposal by Astrakharchik et al for the existence of a super Tonks - Girardeau gas-like state in the attractive interaction regime of quasi-one-dimensional Bose gases. We show that the super Tonks - Girardeau gas-like state corresponds to a highly excited Bethe state in the integrable interacting Bose gas for which the bosons acquire hard-core behaviour. The gas-like state properties vary smoothly throughout a wide range from strong repulsion to strong attraction. There is an additional stable gas-like phase in this regime in which the bosons form two-body bound states behaving like hard-core bosons.