Spin-Imbalanced Quasi-Two-Dimensional Fermi Gases

We measure the density profiles for a Fermi gas of ${}^6\mathrm{Li}$ containing $N_1$ spin-up atoms and $N_2$ spin-down atoms, confined in a quasi-two-dimensional geometry. The spatial profiles are measured as a function of spin imbalance $N_2/N_1$ and interaction strength, which is controlled by means of a collisional (Feshbach) resonance. The measured cloud radii and central densities are in disagreement with mean-field Bardeen-Cooper-Schrieffer theory for a true two-dimensional system. We find that the data for normal-fluid mixtures are reasonably well fit by a simple two-dimensional polaron model of the free energy. Not predicted by the model is a phase transition to a spin-balanced central core, which is observed above a critical value of $N_2/N_1$. Our observations provide important benchmarks for predictions of the phase structure of quasi-two-dimensional Fermi gases.

Figure 1

Top: Side image of layered pancake-shaped atom clouds, separated by $5.3\mu \mathrm{m}$ in a ${\mathrm{CO}}_2$ laser standing-wave trap. Bottom: In each pancake, confinement causes majority spins (blue-up arrow) and minority spins (red-down arrow) to pair, producing bound dimers. Polarons form when minority atoms scatter in the Fermi sea of the majority atoms and become surrounded by a cloud of particle-hole pairs (dark-blue-light-blue). Tightly bound dimers also scatter, forming dressed dimers.

Figure 2

Measured column density profiles in units of $N_1/R_{\mathrm{TF}1}$ at 832 G, for $E_F/E_b=6.6$ (left panel) and at 775 G, for $E_F/E_b=0.75$ (right panel) versus $N_2/N_1$. Green: 1-majority, red: 2-minority. Blue-dashed: Column density difference. Each profile is labeled by its $N_2/N_1$ bin (range $\pm 0.03$). For the density difference, the flat center and two peaks at the edges are consistent with a fully paired core of the corresponding 2D density profiles. These features are more prominent for the higher interaction strength (right panel).

Figure 3

Majority radii (upper-blue) and minority radii (lower-red) in units of the Thomas-Fermi radius for the majority for $E_F/E_b=6.6$ (left panel), $E_F/E_b=2.1$ (middle panel) and $E_F/E_b=0.75$ (right panel). Dots: Data; solid lines: 2D polaron model for imbalanced mixture $0\le N_2/N_1\le 0.9$ [30], 2D polaron model for balanced mixture $N_2/N_1=1$ [30]. Dashed lines: Ideal Fermi gas prediction, black circle upper right: 2D-BCS theory for a balanced mixture.

Figure 4

Reduced 2D pressure at the trap center versus $E_F/E_b$ for the balanced gas. Dots: Experiment, solid red curve: prediction based on the polaron model for the balanced gas, dashed line: prediction of 2D-BCS theory.

Figure 5

Ratio of minority to majority 2D central densities for $E_F/E_b=6.6$ (left panel), $E_F/E_b=2.1$ (middle panel), and for the strongest interactions $E_F/E_b=0.75$ (right panel). Blue dots: data, red solid line: 2D polaron model, dashed black line: ideal Fermi gas prediction. Stronger interactions balance the central densities over an extended range of imbalance, in clear disagreement with the polaron model.