Two-Component Fermi Gas on Internal-State-Dependent Optical Lattices

We study the phase diagram of a one-dimensional, two-component (i.e., pseudo-“spin”-$\frac{1}{2}$) ultracold atomic Fermi gas. The two atom species can have different hopping or mass. A very rich phase diagram for equal densities of the species is found, containing Mott insulators and superfluids. We also discuss coupling such 1D systems and the experimental signatures of the phases. In particular, we compute the spin-structure factor at small momentum, which should reveal a spin gap.

Figure 1

Schematic phase diagram for the model of Eq. (1) with equal number of spin-up and -down fermions away from half filling (i.e., $N_{\uparrow 0}=N_{\downarrow 0}\ne M/2$). $U$ is the interaction strength and $z=|t_{\uparrow }-t_{\downarrow }|/(t_{\uparrow }+t_{\downarrow })$. All phases (SDW: spin-density wave, CDW: charge density wave, SS: singlet superfluid, TS: triplet superfluid) exhibit a spin gap ${\Delta }_s$, except ${\Delta }_s=0$ for $U=0$ (FG: Fermi gas) and $z=0$ for $U>0$ (TLL: Tomonaga-Luttinger liquid). The first acronym refers to the dominant type of order, the second (in parentheses) to the subdominant one (see text for explanations). A cartoon of the dominant order in each phase is also shown. In the area between dashed lines the dominant order (either CDW or SS) depends on the lattice filling (see text). In the SG phase, spin-up and -down fermions are segregated (demixed).