  We study an effect of rotation on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
state of two component Fermi superfluid gases in a toroidal trap. We
investigate a stability of the FFLO states in the quasi-one-dimensional regime
on the basis of the Bogoliubov-de Gennes equation. We find that two novel FFLO
phases, i.e., the half quantum vortex state and the intermediate state of
Fulde-Ferrell (FF) state and Larkin-Ovchinnikov (LO) state, are stabilized by
the rotation. The phase diagram for the FF state, LO state, intermediate state,
and half quantum vortex state is shown in both T-P plane and T-h plane. We
demonstrate characteristic features of these states, such as the order
parameter, flux quantization, and local polarization. Several related works are
discussed, and the advantages of cold Fermi gases are indicated.
