Sarma Phase in Trapped Unbalanced Fermi Gases

We consider a trapped unbalanced Fermi gas at nonzero temperatures where the superfluid Sarma phase is stable. We determine, in particular, the phase boundaries between the superfluid, normal, and phase-separated regions of the trapped unbalanced Fermi mixture. We show that the physics of the Sarma phase is sufficient to understand the recent observations of Zwierlein et al. [Science 311, 492 (2006); Nature (London) 442, 54 (2006)] and indicate how the apparent contradictions between this experiment and the experiment of Partridge et al. [Science 311, 503 (2006)] may be resolved.

Figure 1

Universal phase diagram of a trapped unbalanced Fermi gas in the unitarity limit. The polarization $P$ is given by $(N_{+}-N_{-})/(N_{+}+N_{-})$, where $N_{\pm }$ designates the number of fermions in each hyperfine state of the Fermi mixture. The temperature $T$ is scaled with the critical temperature $T_c$ of the balanced Fermi gas. The solid horizontal line gives the temperature that is used for the comparison with the experiments of Zwierlein et al. presented in Figs. 2, 3. The points a, b, and c correspond to the polarizations used in the density profiles of Figs. 2a, 2b, 2c.

Figure 2

Typical density profiles for trapped unbalanced Fermi gas above the tricritical point. The axial and radial directions of the trap are scaled in such a manner that the trap becomes effectively isotropic with a frequency $\omega =({\omega }_{\perp }^2{\omega }_z{)}^{1/3}$ and a size $l=(\hslash /m\omega {)}^{1/2}$. The temperature and the polarizations used for the three panels are indicated in Fig. 1. The total number of atoms is $N=1.4\times {10}^7$. The dashed lines in (c) show the ideal gas results.

Figure 3

The radial size $R$ of the Cooper-pair condensate (solid line), and the minority (dashed line) and majority (dotted-dashed line) gas clouds as a function of polarization for the temperature shown in Fig. 1. All radial sizes are scaled with the radial Thomas-Fermi radius of the balanced Fermi gas $R_{\mathrm{TF}}$. Also shown are the experimental data of Zwierlein et al. [5]. For the radial size of the majority cloud, the black points assume a hydrodynamic expansion, whereas the gray points assume a ballistic expansion.