Superfluid-ferromagnet-superfluid junction and the π phase in a superfluid Fermi gas

We investigate the possibility of a superfluid-ferromagnet-superfluid (SFS) junction in a superfluid Fermi gas. To examine this possibility in a simple manner, we consider an attractive Hubbard model at T=0 within the mean-field theory. When a potential barrier is embedded in a superfluid Fermi gas with population imbalance (N↑>N↓, where Nσ is the number of atoms with pseudospin σ= ↑, ↓), this barrier is shown to be magnetized in the sense that excess ↑-spin atoms are localized around it. The resulting superfluid Fermi gas is spatially divided into two by this ferromagnet, so that one obtains a junction similar to the superconductor- ferromagnet-superconductor junction discussed in superconductivity. Indeed, we show that the so-called π phase, which is a typical phenomenon in the SFS junction, is realized, where the superfluid order parameter changes its sign across the junction. Our results would be useful for the study of magnetic effects on fermion superfluidity using an ultracold Fermi gas.