Confinement and superfluidity in one-dimensional degenerate fermionic cold atoms

The physical properties of arbitrary half-integer spins F=N-1/2 fermionic cold atoms trapped in a one-dimensional optical lattice are investigated by means of a low-energy approach. Two different superfluid phases are found for F >= 3/2 depending on whether a discrete symmetry is spontaneously broken or not: an unconfined BCS pairing phase and a confined molecular-superfluid instability made of 2N fermions. We propose an experimental distinction between these phases for a gas trapped in an annular geometry. The confined-unconfined transition is shown to belong to the Z(N) generalized Ising universality class. We discuss the possible Mott phases at 1/2N filling.