Phase Separation and Pair Condensation in a Spin-Imbalanced 2D Fermi Gas

We study a two-component quasi-two-dimensional Fermi gas with imbalanced spin populations. We probe the gas at different interaction strengths and polarizations by measuring the density of each spin component in the trap and the pair momentum distribution after time of flight. For a wide range of experimental parameters, we observe in-trap phase separation characterized by the appearance of a spin-balanced core surrounded by a polarized gas. Our momentum space measurements indicate pair condensation in the imbalanced gas even for large polarizations where phase separation vanishes, pointing to the presence of a polarized pair condensate. Our observation of zero momentum pair condensates in 2D spin-imbalanced gases opens the way to explorations of more exotic superfluid phases that occupy a large part of the phase diagram in lower dimensions.

Figure 1

Experimental setup. (a) A 1D optical lattice is formed at the intersection of two interfering blue-detuned beams (green), providing axial confinement. The lattice spacing can be dynamically tuned by changing the angle between the beams. The atoms are radially confined by a red-detuned beam (brown) in the vertical direction. A high-NA objective (gray) is used to image the in-plane density distribution. The inset shows a section of the optical potential with color scale from red (attractive) to blue (repulsive). (b) Side absorption images illustrating our capability to load and resolve single (above) and multiple pancakes (below) after adiabatically increasing the lattice spacing to $\sim 12\mu \mathrm{m}$. (c) In situ absorption images of majority (above) and minority (below) clouds along the vertical direction at 755 G and polarization $P=0.6$.

Figure 2

Phase separation and condensation vs global polarization. (a)–(c) Azimuthal average of in situ OD of majority (yellow) and minority (red) clouds, and of their difference (blue) for $P=0.25$, 0.55, and 0.75, respectively, taken at a field of 780 G, with fits to the sum of a Gaussian and a Thomas-Fermi profile. The insets show the corresponding two-dimensional OD difference. The gray shaded region represents the systematic error in the determination of OD differences. The radial position is measured along the minor axis of the elliptical contour lines used for azimuthal averaging. (d)–(f) OD of the minority cloud after 3 ms time of flight normalized to its peak value, with a double Gaussian fit to the data. The thermal component is shaded in red, while the condensate is shaded in gray. Error bars represent the standard deviation of the mean in evaluating the azimuthal average. All distributions represent an average of 30 experimental realizations.

Figure 3

Central polarization and condensate fraction vs global polarization. Central polarization (blue diamonds) and condensate fraction (yellow circles) are shown for the Feshbach fields of (a) 730, (b) 755, (c) 780, (d) 830, and (e) 920 G. The points represent the average of 5–15 experimental realizations, and error bars are the standard deviation of the mean. The gray region indicates the experimental uncertainty in the determination of the central polarization. The blue line is a bilinear fit to the data to determine $P_c$. For condensate fraction data, each point is obtained from a bootstrap analysis of 30 experimental shots. Error bars represent the standard deviation of the bootstrap distribution. The insets show the OD difference at $P=0.25$ and 0.75.

Figure 4

Critical polarization ($P_c$) for phase separation vs $E_B/E_F$ (log-scale). The global polarization at which phase separation ends is extracted from a bilinear fit to the central polarization data in Fig. 3 (red diamonds). Corresponding magnetic fields for these points are shown on the secondary $x$ axis. For comparison, we extracted two points from the data of Ref. [42] (blue squares). The error bars are given by the fit uncertainty.

Figure 5

Phase diagram of an imbalanced 2D Fermi gas for four different interactions determined by the Feshbach fields (a) 730, (b) 755, (c) 780, and (d) 830 G. The corresponding interaction strengths $E_B/E_F$ are shown in the top-right corner of each panel. The color indicates the local polarization of the gas in the trap $p(r)$ as a function of the scaled position in the trap $r/R_{\mathrm{TF}\uparrow }$ and the global polarization $P$. We distinguish three different phases: a balanced condensate (red), a partially polarized phase (white to gray), and a fully polarized normal gas (blue).