Chandrasekhar-Clogston limit and critical polarization in a Fermi-Bose superfluid mixture

We study mixtures of a population-imbalanced, strongly interacting Fermi gas and of a Bose-Einstein condensed gas at zero temperature. In the homogeneous case, we find that the Chandrasekhar-Clogston critical polarization for the onset of instability of Fermi superfluidity is enhanced due to the interaction with the bosons. Predictions for the critical polarization are also given in the trapped case, with a special focus on the situation of equal Fermi-Bose and Bose-Bose coupling constants, where the density of fermions becomes flat in the center of the trap. This regime can be realized experimentally using Feshbach resonances and is well suited to investigate the emergence of exotic configurations, such as the occurrence of spin domains or the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase.