  We study equal mass population imbalanced two-component atomic Fermi gas with
unequal trap frequencies $(\omega_{\uparrow} \neq \omega_{\downarrow})$ 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.
