Universal Phase Diagram and Scaling Functions of Imbalanced Fermi Gases

Abstract

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 $\mu$ and effective magnetic field $h$, first discussed by Nikoli\'{c} 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 $T/\mu$ and $h/\mu$. The results indicate that beyond the Clogston-Chandrasekhar limit at $(h/\mu)_c\simeq 1.09$, the unitary gas exhibits an inhomogeneous superfluid phase with FFLO order that can reach critical temperatures near unitarity of $\simeq 0.03\, T_F$.