The name is absent

24

with each other. In fact, this matching of the radial profiles occur for ∣z∣ ≤ 0.1. As a
consequence, the axial spin density vanishes near z = 0 as shown in the upper subplot in
the left column of Fig. 3.2, which is a clear signature of the breakdown of the LDA.

The reason why the majority and minority densities overlap along the radial direction
can be understood from the surface energy point of view. When phase separation occurs,
there is an accompanying surface energy associated with the interface between the two
phases. The system will then try to minimize the interface area in order to reduce the
surface energy. For a cigar-like trap as we studied here, the superfluid-normal gas interface
area can be efficiently reduced if the two spin components match their densities radially.
The authors of Ref. [26, 27] devised phenomenological theories to include the surface term
Variationally to explain the breakdown of the LDA observed in Rice experiment [18]. In
our calcultion, the surface energy is automatically included from the self-consistent BdG
solution.

As polarization increases, eventually it becomes energetically unfavorable to have this
radial density matching. This is illustrated in Fig. 3.3(b) for P = 0.6. Consequently, the
axial spin density no longer vanishes near z = 0, but still shows a dip (see the middle
and lower subplots in the left column of Fig. 3.2). In addition, it is quite noticable that
the minority component density has a much steeper down turn along the axial axis than
along the radial axis. Moreover, in the partially polarized intermediate region, the order
parameter has a small oscillation along the axial axis, but not along the radial axis. Similar
order parameter oscillations were also found in the spherical trap case [22].

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