The name is absent

26

A consequence of the breakdown of the LDA is that the atomic cloud aspect ratio will
deviate from the trap aspect ratio as shown in the Rice experiment [18]. In Fig. 3.4, we
present the cloud aspect ratio as a function of polarization from our calculation. We define
the cloud aspect ratio as κ_σ =   ∕R⅛ with

_ fzn<_r(p = 0,z)dz
f^,                                    9

~ J n_σ(ρ = 0, z) dz

and similarly for R⅛. Within the LDA, both κ↑ and κ_l are very close to the trap aspect ratio
Λ and are insensitive to the polarization. Fig. 3.4(a) shows the BdG results for the trap
with Λ = 5. For a population balanced system (P = 0), we have ∕c↑ ~ κ_i, ≈ 4.85 which is
close to the trap aspect ratio. As P increases from zero, κ↑ increases while ∕q decreases. In
other words, the majority component stretches along the axial direction, while the minority
component bulges along the radial direction, such that their radial density profiles match
with each other in order to reduce the interface area, as we discussed above.

Figure 3.4(b) shows the cloud aspect ratio in the very elongated trap with Л = 50.
For this trap, the majority and minority components have their densities matched along
the radial axis up to the highest polarization we have calculated which is P - 0.7. This
further confirms that the system is able to greatly reduce the effective surface area between
the normal state and the superfluid state in anisotropic cigar-like traps. Another marked
feature for such an elongated trap is the damped oscillations in the order parameter along
the z-axis. As demonstrated in Fig. 3.5, these oscillations are quite generic features in such
a trap with finite P. As P increases, both the amplitude and the spatial extension of the
oscillation increase. As shown in Fig. 3.5(b), at large polarizations, the axial length of the

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