  We study the angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which
the rotation symmetry is spontaneously broken, in population imbalanced fermion
gases. The superfluid gases at near T=0 are investigated on the basis of the
Bogoliubov-de Gennes (BdG) equation. We find that the angular FFLO state is
stabilized in the gases confined in the toroidal trap, but not in the harmonic
trap. We discuss the mechanism of the angular FFLO state based on the
self-one-dimensionalization of the superfluid gas.
