  We demonstrate that a kind of highly excited state of strongly attractive
Hubbard model, named of Fermi super-Tonks-Girardeau state, can be realized in
the spin-1/2 Fermi optical lattice system by a sudden switch of interaction
from the strongly repulsive regime to the strongly attractive regime. In
contrast to the ground state of the attractive Hubbard model, such a state is
the lowest scattering state with no pairing between attractive fermions. With
the aid of Bethe-ansatz method, we calculate energies of both the Fermi
Tonks-Girardeau gas and the Fermi super-Tonks-Girardeau state of spin-1/2
ultracold fermions and show that both energies approach to the same limit as
the strength of the interaction goes to infinity. By exactly solving the quench
dynamics of the Hubbard model, we demonstrate that the Fermi
super-Tonks-Girardeau state can be transferred from the initial repulsive
ground state very efficiently. This allows the experimental study of properties
of Fermi super-Tonks-Girardeau gas in optical lattices.
