Universal Phase Diagram and Scaling Functions of Imbalanced Fermi Gases

We discuss the phase diagram and the universal scaling functions of attractive Fermi gases at finite imbalance. The existence of a quantum multicritical point for the unitary gas at vanishing chemical potential μ and effective magnetic field h, first discussed by Nikolić and Sachdev, gives rise to three different phase diagrams, depending on whether the inverse scattering length 1/a is negative, positive or zero. Within a Luttinger–Ward formalism, the phase diagram and pressure of the unitary gas is calculated as a function of the dimensionless scaling variables T/μ and h/μ. The results indicate that beyond the Clogston–Chandrasekhar limit at (h/μ)_c ≃ 1.09, the unitary gas exhibits an inhomogeneous superfluid phase with FFLO order that can reach critical temperatures near unitarity of ≃0.03T_F .