Universal phase diagram and scaling functions of imbalanced Fermi gases

TL;DR

This paper explores the phase diagram and universal scaling functions of imbalanced Fermi gases, revealing a quantum multicritical point and the existence of an inhomogeneous superfluid phase with FFLO order near unitarity.

Contribution

It provides a comprehensive analysis of the phase diagram at unitarity considering different scattering lengths and introduces a Luttinger-Ward formalism to calculate pressure and phase boundaries.

Findings

Identification of a quantum multicritical point at unitarity.

Prediction of an inhomogeneous FFLO superfluid phase beyond the Clogston-Chandrasekhar limit.

Critical temperature of the FFLO phase reaches about 0.03 T_F near unitarity.

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 $\simeq 0.03\, T_F$.