Homogeneous Atomic Fermi Gases

We report on the creation of homogeneous Fermi gases of ultracold atoms in a uniform potential. In the momentum distribution of a spin-polarized gas, we observe the emergence of the Fermi surface and the saturated occupation of one particle per momentum state: the striking consequence of Pauli blocking in momentum space for a degenerate gas. Cooling a spin-balanced Fermi gas at unitarity, we create homogeneous superfluids and observe spatially uniform pair condensates. For thermodynamic measurements, we introduce a hybrid potential that is harmonic in one dimension and uniform in the other two. The spatially resolved compressibility reveals the superfluid transition in a spin-balanced Fermi gas, saturation in a fully polarized Fermi gas, and strong attraction in the polaronic regime of a partially polarized Fermi gas.

Figure 1

Homogeneous Fermi gas. (a) Schematic of the box trap and cuts through the column-integrated density profiles along the axial and radial directions. (b) Radius of the cloud as a function of the Fermi energy. The dotted black and dashed red lines correspond to a perfect box potential and a harmonic potential, respectively, and are scaled to converge at the highest $E_F$. The blue solid line corresponds to a power law potential $V(r)\sim r^{16}$. (c) Measured radial probability density $\mathcal{P}(n_{2\mathrm{D}})$ for the column-integrated density $n_{2\mathrm{D}}$, averaging about 20 in-trap images. The blue solid and red dashed lines correspond to the uniform and Gaussian traps, respectively.

Figure 2

Momentum distribution of the homogeneous spin-polarized Fermi gas. (a) Doubly integrated momentum distribution $f_{1\mathrm{D}}$ for different temperatures in the uniform trap. In order of decreasing temperature: red dotted line, orange dashed line, and blue solid line. Each line corresponds to averages over seven images. The optical density after momentum space mapping along $z$ is shown in the inset. (b),(c),(d) Momentum distribution $f_k=-4\pi d{f}_{1\mathrm{D}}/d{k}^2$, showing Pauli blocking and Fermi surface formation. Fermi-Dirac fits (solid line) give (b) $T/T_F=0.49(2)$, (c) $T/T_F=0.32(1)$, and (d) $T/T_F=0.16(1)$, with $k_F$ ranging between $2.8{\mu \mathrm{m}}^{-1}$ and $3.7{\mu \mathrm{m}}^{-1}$. The estimated systematic error in the measurement of $f_k$ is 15%.

Figure 3

Pair condensation in the uniform trap. (a), (b), and (c) Absorption images after a rapid ramp of the magnetic field and 10 ms of time of flight. The temperature of the gas is lowered (left to right) by evaporation in the uniform trap. The onset of a bimodal distribution signals the formation of a pair condensate. (d), (e), and (f) show cuts through the images in the top row.

Figure 4

Unitary Fermi gases in the hybrid trap. (a) Schematic and potential of the trap. The cloud is imaged along an equipotential direction ($x$ axis). Left panels of (b)–(e) show a spin-imbalanced gas above the Clogston-Chandrasekhar limit, whereas the right side corresponds to a spin-balanced gas. The data are averaged over six images. (b) Local density for both spin components, obtained by dividing the column density by the column length. (c) Average density for each $x\text{−}y$ equipotential slice. The blue (red) line shows the spin-up (-down) component. (d) Spatially resolved temperature of the gas. The blue shaded region represents the error in the temperature determination. (e) Compressibility of the gas. The solid line in the left panel is the compressibility for an ideal Fermi gas. The crossover from the fully polarized (FP) region to the partially polarized (PP) region is accompanied by an increase in $\tilde{\kappa }$. The yellow squares in the right panel correspond to a precision measurement of the balanced unitary equation of state in the harmonic trap [31]. The peaks in the compressibility signal the phase transition from normal (N) to superfluid (SF). The horizontal dashed line shows the zero-temperature equation of state $\kappa /{\kappa }_0=1/\xi$.