Abstract
We investigate transition of a one-dimensional interacting Bose gas from a strongly repulsive regime to a strongly attractive regime, where a stable highly excited state known as the super Tonks-Girardeau gas was experimentally realized very recently. By solving exact dynamics of the integrable Lieb-Liniger Bose gas, we demonstrate that such an excited gas state can be a very stable dynamic state. Furthermore we calculate the breathing mode of the super Tonks-Girardeau gas which is found to be in good agreement with experimental observation. Our results show that the highly excited super Tonks-Girardeau gas phase can be well understood from the fundamental theory of the solvable Bose gas.
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