Fulde-Ferrell superfluids in an asymmetric three-component Fermi Gas

Abstract

An asymmetric three-component Fermi gas, featuring Raman-induced spin-orbit coupling between the first and second components and contact interaction only between the first and third components, introduces both spin-orbit coupling and population imbalance-two mechanisms known to stabilize the Fulde-Ferrell superfluids.We systematically study Fulde-Ferrell superfluids in an asymmetric three-component Fermi gas by finding the global minima of the thermodynamic potential. We reveal a new class of composite Fulde-Ferrell superfluids that emerges when strong spin-orbit coupling generates a double-well structure in momentum space within the lower spin-orbit-coupled band. The key features of these composite superfluids are identified.

Figures (3)

• Figure 1: FF pairs in an asymmetric three-component Fermi gas with weak SOC, $\alpha=1$, $h=1$, and $E_{b,13}=0.5$. (a) Single-particle dispersion of $H_0(\bm{k})$ as a function of $k_x$ for $k_y=0$. The isolated energy band of the third component is shown by the black line. The spin-orbit-coupled energy bands of the first and second components are shown by the colored lines. The red (blue)-colored parts emphasize the dominant occupation of the first (second) component. The green-dashed horizontal line represents $\mu_{12}=1.1$, which cuts through both the spin-orbit-coupled bands, generating an upper-band state (labeled by a green open circle) and a lower-band state (labeled by a green solid circle). The chemical potential $\mu_3$ cuts through the third-component band, resulting in two states (labeled by purple open and solid circles). (b) Phase diagram showing the evolution of $\Delta_{13}$ (blue solid line) and $Q_x$ (red-dashed line) of the ground states as functions of $\mu_3$. The diagram includes the normal phase (N, light blue region), the FF1 phase (light red region), and the FF2 phase (light green region). The inset shows a zoom-in of $Q_x$ in the FF1 phase. (c) and (d) show the thermodynamic potential $\Omega$ in the parameter space of $(\Delta_{13}, Q_x)$ for $\mu_3 = 0.1$ and $\mu_3 = 0.8$, respectively. The global minimum of the thermodynamic potential is labeled by a red circle.
• Figure 2: FF pairs in an asymmetric three-component Fermi gas with strong SOC, $\alpha=3$, $h = 0.8$, and $E_{b,13} = 0.5$. The left panels show the single-particle energy bands, and the right panels show the corresponding phase diagrams. (a1) and (a2) $\mu_{12} = 1.5$ cuts through both spin-orbit-coupled bands. (b1) and (b2) $\mu_{12} = 0.2$ lies within the spin-orbit coupling gap. The insets in (a2) and (b2) provide zoomed-in views of $Q_x$ to illustrate its variation. (c1) and (c2) $\mu_{12} = -1.5$ cuts through the double-well structure within the lower spin-orbit-coupled band. The new composite FF phase, labeled "CFF", is shown in the light yellow region.
• Figure 3: Phase diagram in the ($E_{b,13},\mu_3$) plane. The parameters are the same as those in Fig. \ref{['Stronge']} with $\mu_{12}=-1.5$.