Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations

We present a theoretical interpretation of a recent experiment presented by Zwierlein et al. [Nature (London) 442, 54 (2006)] on the density profile of Fermi gases with unbalanced spin populations. We show that in the regime of strong interaction, the boundaries of the three phases observed by Zwierlein et al. can be characterized by two dimensionless numbers η_α and η_β. Using a combination of a variational treatment and a study of the experimental results, we infer rather precise bounds for these two parameters.