Trap and population imbalanced two-component Fermi gas in the BEC limit

We study equal mass population imbalanced two-component atomic Fermi gas with unequal trap frequencies $({\omega }_{\uparrow }\mathrm{\ne }{\omega }_{\downarrow })$ at zero temperature using the local density approximation (LDA). We consider the strongly attracting Bose-Einstein condensation (BEC) limit where polarized (gapless) superfluid is stable. The system exhibits shell structure: unpolarized SF$\to$polarized SF$\to$normal N. Compared to trap symmetric case, when the majority component is tightly confined the gapless superfluid shell grows in size leading to reduced threshold polarization to form polarized (gapless) superfluid core. In contrast, when the minority component is tightly confined, we find that the superfluid phase is dominated by unpolarized superfluid phase with gapless phase forming a narrow shell. The shell radii for various phases as a function of polarization at different values of trap asymmetry are presented and the features are explained using the phase diagram.