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

We present a theoretical interpretation of a recent experiment presented in ref. \cite{Zwierlein06} 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 in \cite{Zwierlein06} can be characterized by two dimensionless numbers $\eta\_\alpha$ and $\eta\_\beta$. Using a combination of a variational treatment and a study of the experimental results, we infer rather precise bounds for these two parameters.