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 $F\ge 3/2$ 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 ${\mathbb{Z}}_N$ generalized Ising universality class. We discuss the possible Mott phases at $1/2N$ filling.

Figure 1

Phase diagram of model (2). Dashed lines denote crossover lines, whereas the solid line marks the phase transition in the ${\mathbb{Z}}_N$ universality class between phase II and phase III.