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 (${N}_{\ensuremath{\uparrow}}>{N}_{\ensuremath{\downarrow}}$, where ${N}_{\ensuremath{\sigma}}$ is the number of atoms with pseudospin $\ensuremath{\sigma}= \ensuremath{\uparrow}$, $\ensuremath{\downarrow}$), this barrier is shown to be magnetized in the sense that excess $\ensuremath{\uparrow}$-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 $\ensuremath{\pi}$ 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.
We present a microscopic theory for superfluidity in an interacting many-particle Bose system (such as liquid
4He). We show that, similar to superconductivity in superconductors, superfluidity in a Bose system arises from pairing of particles of opposite momenta. We show the existence of an energy gap in single-particle excitation spectrum in the superfluid state and the existence of a specific heat jump at the superfluid transition. We derive an expression for superfluid particle density
ns as a function of temperature
T and superfluid velocity
vs. We show that superfluid-state free energy density
F is an increasing function of
vs (i.e.,
∂F/∂vs>0), which indicates that a superfluid has a tendency to remain motionless (this result qualitatively explains the Hess-Fairbank effect, which is analogous to the Meissner effect in superconductors). We further speculate the existence of the equation ${\bf j}=-Λ\nabla\times \text{\boldmath
ω}$, where
j=nsvs is the superfluid current density, $\text{\boldmath
ω}=\nabla\times {\bf v}_s$ the superfluid vorticity, and
Λ a positive constant (with the help of this equation, the Hess-Fairbank effect can be quantitatively described).
The spin superfluidity -- superfluidity in the magnetic subsystem of a condensed matter - is manifested as the spontaneous phase-coherent precession of spins first discovered in 1984 in 3He-B. This superfluid current of spins - spin supercurrent - is one more representative of superfluid currents known or discussed in other systems, such as the superfluid current of mass and atoms in superfluid 4He; superfluid current of electric charge in superconductors; superfluid current of hypercharge in Standard Model of particle physics; superfluid baryonic current and current of chiral charge in quark matter; etc. Spin superfluidity can be described in terms of the Bose condensation of spin waves - magnons. We discuss different phases of magnon superfluidity, including those in magnetic trap; and signatures of magnons superfluidity: (i) spin supercurrent, which transports the magnetization on a macroscopic distance more than 1 cm long; (ii) spin current Josephson effect which shows interference between two condensates; (iii) spin current vortex - a topological defect which is an analog of a quantized vortex in superfluids, of an Abrikosov vortex in superconductors, and cosmic strings in relativistic theories; (iv) Goldstone modes related to the broken U(1) symmetry - phonons in the spin-superfluid magnon gas; etc. We also touch the topic of spin supercurrent in general including spin Hall and intrinsic quantum spin Hall effects.