Phase Diagram of a $$^6Li$$ 6 L i – $$^{40}K$$ 40 K Mixture in a Square Lattice

Abstract

We calculate the mean-field phase diagram for an attractive interacting Fermi mixture of Lithium-6 ( $$^6Li$$ ) and Potassium-40 ( $$^{40}K$$ ) atoms in a two-dimensional optical lattice at finite temperatures. The polarization versus temperature diagrams show that there are three phases: the Sarma phase (in which the condensed pairs have zero net momentum), the Fulde–Ferrell (FF) phase (in which the pairs have non-zero net momentum), and the normal phase (in which the Helmholtz free energy is minimized for gapless phase). The zero polarization line is the conventional Bardeen–Cooper–Schrieffer state. The phase diagram contains a Lifshitz point. When the interaction strength is increased, the Lifshitz point moves toward the higher temperatures and larger polarizations. Moreover, contrary to the phase diagram of population-imbalanced $$^6Li$$ Fermi gas, where the phase separation appears for low polarizations, we found the existence of a polarization window for the FF phase. This means that as soon as the system is polarized it goes into the FF phase if the temperature is low enough. This polarization window is larger for a majority of $$^{40}K$$ atoms compared to the majority of $$^6Li$$ atoms. We also find that the largest polarization that the system can support before it becomes a normal fluid is larger for majority of $$^6Li$$ atoms.