Phase diagram of a cold polarized Fermi gas

We propose a phase diagram for a cold polarized atomic Fermi gas with zero-range interaction. We identify four main phases in the plane of density and polarization: the superfluid phase, the normal phase, the gapless superfluid phase, and the modulated phase. We argue that there exists a Lifshitz point at the junction of the normal, the gapless superfluid, and the modulated phases, and a splitting point where the superfluid, the gapless superfluid, and the modulated phases meet. We show that the physics near the splitting point is universal and derive an effective field theory describing it. We also show that subregions with one and two Fermi surfaces exist within the normal and the gapless superfluid phases.

Figure 1

The proposed phase diagram in the plane of the diluteness parameter $\kappa =-1∕\left(n{a}^3\right)$ and the (scaled) polarization chemical potential $\eta =H∕{\Delta }_{H=0}$. I is the unpolarized BEC or BCS phase, II is the normal phase, III is the gapless superfluid phase, and IV is a region of Fulde-Ferrell-Larkin-Ovchinnikov phases. The dashed line divides phases II and III into regions with one (on the left) and two (on the right) Fermi surfaces. Region IV must be divided into phases with different patterns of breaking of the rotational symmetry (not shown).

Figure 2

Spectrum of fermionic quasiparticles at $\eta =0$ for $\kappa <{\kappa }_0$ (left) and for $\kappa >{\kappa }_0$ (right). The minimum is located at $p=0$ for $\kappa <{\kappa }_0$ and $p\ne 0$ for $\kappa >{\kappa }_0$.

Figure 3

(Color online) Function $f_h\left(x\right)$ at three representative values of $h$.

Figure 4

Occupied fermion quasiparticle modes in phase IV near point $S$ occupy a thin spherical cap with curvature radius $p=\sqrt{\alpha ∕\left(2\beta \right)}$. The angle $\theta$ increases from $80.4^{\circ }$ at $\eta ={\eta }_1+0$ to $127.3^{\circ }$ at $\eta ={\eta }_2-0$.

Figure 5

Occupied quasifermion modes ($p_z=0$ cross section) near point $S$ in phase IV (a) and in phase III (b),(c).