Trapped two-dimensional Fermi gases with population imbalance

We study population imbalanced Fermi mixtures under quasi-two-dimensional confinement at zero temperature. Using mean-field theory and the local density approximation, we study the ground state configuration throughout the BEC-BCS crossover. We find the trapped system to be either fully normal (throughout the trap) or to consist of a superfluid core phase surrounded by a normal shell, which is itself either fully or partially polarized. Upon changing the trap imbalance, the entire trap configuration may undergo continuous or discontinuous transitions between the different ground states. We establish the phase diagrams for trapped situations both with and without a surface tension. The latter is found to strongly favor the fully polarized normal phase. We also study the collective excitations of the system and find discontinuities of the frequency spectra at the discontinuous transition point. There also appear modes with oscillation frequencies below the trapping frequency. Finally, we argue that thermal equilibration throughout the trap will be considerably slowed down at low temperatures when a superfluid phase is present.