Mean-field phase diagrams of imbalanced Fermi gases near a Feshbach resonance

We propose phase diagrams for an imbalanced (unequal number of atoms or Fermi surface in two pairing hyperfine states) gas of atomic fermions near a broad Feshbach resonance using mean-field theory. Particularly, in the plane of interaction and polarization we determine the region for a mixed phase composed of normal and superfluid components. We compare our prediction of phase boundaries with the recent measurement and find a good qualitative agreement.

Figure 1

(Color online) Landscape of the thermodynamic potential at $1∕k_{F}a=-1$. The chemical potential is fixed to $\mu =0.98942{ϵ}_F$. The competing ground states are (i) a normal Fermi gas with $\Delta =0$, (ii) a fully paired BCS superfluid with $\Delta ={\Delta }_0$, $q=0$, and $\delta n=0$, (iii) a breached pairing or Sarma superfluid with $\Delta <{\Delta }_0$, $q=0$, and $\delta n\ne 0$, (iv) a finite momentum paired FFLO superfluid with $\Delta <{\Delta }_0$, $q\ne 0$, and $\delta n\ne 0$, and (v) a saddle point phase intervening between the local BCS and FFLO minima.

Figure 2

(Color online) Phase diagram in the plane of interaction and chemical potential difference.

Figure 3

(Color online) Comparison of free energies of available mean-field solutions at coupling constants as indicated, with the free energy of the normal gas $F_0$ being subtracted. $E_c=\mathcal{N}\left(0\right){\Delta }_{\mathit{BCS}}^2∕2$ is the condensation energy for a symmetric Fermi gas, $\mathcal{N}\left(0\right)=m{k}_F∕\left(2{\pi }^2{\hslash }^2\right)$ is the density of state at the Fermi surface and ${\Delta }_{\mathit{BCS}}=8\exp [\pi ∕\left(2k_{F}a\right)-2]$.

Figure 4

(Color online) Comparison of energies of competing phases. Insets show the chemical potential difference as a function of polarization. The arrow in the inset of (b) indicates a position, above which the slope of the curve becomes positive.

Figure 5

(Color online) Interaction-porlarization phase diagram. The superfluid-to-normal transition boundary (thick line) is to be compared with the experimental data (symbols). The shadowed region is unstable against phase separation.