  Fermi gases confined in tight one-dimensional waveguides form two-particle
bound states of atoms in the presence of a strongly attractive interaction.
Based on the exact solution of the one-dimensional spin-1/2 interacting Fermi
gas, we demonstrate that a stable excited state with no pairing between
attractive fermionic atoms can be realized by a sudden switch of interaction
from strongly repulsive regime to the strongly attractive regime. Such a state
is an exact fermionic analog of the experimentally observed
super-Tonks-Girardeau state of bosonic Cesium atoms [Science 325, 1224 (2009)]
and should be possible to be observed by the experiment. The frequency of
lowest breathing mode of the fermionic super-Tonks-Girardeau gas is calculated
as a function of the interaction strength, which could be used as a detectable
signature for the experimental observation.
