22
a much weaker cylindrical symmtry. The density profiles indicate a phase-separation sce-
nario: a fully paired BCS superfluid core at the trap center surrounded by a fully polarized
shell composed of excess majority spins. A thin layer of partially polarized gas forms the
interface between the superfluid core and the normal shell. In this intermidiate regime, the
minority density and the order parameter quickly drops to zero. Here and in other cases,
we always found that the profile of the order parameter closely follows that of the density
of the minority spin component. Furthermore, in this case, the LDA gives very good agree-
ment with the full BdG calculation. In particular, the axial spin density from BdG shows a
flat-topped structure, consistent with the prediction from the LDA [25].
Let us now turn our attention to the left column of Fig. 3.2, representing results ob-
tained for a cigar-like potential with trap aspect ratio Λ - 5. Here we can immediately see
the striking difference in density profiles in comparison to the spherical trap system. In par-
ticular, the axial spin denisties exhibit a two-peaked structure, indicating a clear violation
of the LDA.
To get a closer look, we plot in Fig. 3.3 the densities and the order paramters along
the axial and radial axis for two different polarizations. Fig. 3.3(a) displays results for
a relatively small polarization with P = 0.2. The density profiles along the z-axis show
clearly a phase separated three-region structure — moving from the center to the edge of
the trap, we encounter a fully paired superfluid core, a partially paired intermediate region
and a fully polarized normal gas, just like in the previous case of spherical trap. In stark
contrast, the density profiles for the two components along the р-axis completely overlap