Reaching Fermi Degeneracy via Universal Dipolar Scattering

We report on the creation of a degenerate dipolar Fermi gas of erbium atoms. We force evaporative cooling in a fully spin-polarized sample down to temperatures as low as 0.2 times the Fermi temperature. The strong magnetic dipole-dipole interaction enables elastic collisions between identical fermions even in the zero-energy limit. The measured elastic scattering cross section agrees well with the predictions from the dipolar scattering theory, which follow a universal scaling law depending only on the dipole moment and on the atomic mass. Our approach to quantum degeneracy proceeds with very high cooling efficiency and provides large atomic densities, and it may be extended to various dipolar systems.

Figure 1

Time-of-flight absorption image of a degenerate Fermi gas of Er atoms at $T/T_F=0.21(1)$ after $t_{\mathrm{TOF}}=12\mathrm{ms}$ of expansion (a) and its density distribution integrated along the $z$ direction (upper panel) and $x$ direction (lower panel) (b). The observed profiles (circles) are well described by fitting a polylogarithmic function to the data (solid lines), while they substantially deviate from a fit using a Gaussian distribution to the outer wings of the cloud, i.e., $w$ (dashed lines). The absorption image is averaged over six individual measurements.

Figure 2

Evaporation trajectory to Fermi degeneracy. (a) Temperature evolution during the evaporation ramp and (b) corresponding $T/T_F$ versus $N$. The ratio $T/T_F$ is obtained from the width $\sigma$ of the distribution (triangles) and from the fugacity (circles); see the text. The error bars originate from statistical uncertainties in temperature, number of atoms, and trap frequencies for the width measurements and the standard deviations obtained from several independent measurements for the fugacity. The solid line is a linear fit to the data for $0.2<T/T_F<4$.

Figure 3

Absorption images of the atomic cloud with a Stern-Gerlach separation of the spin components. A magnetic field gradient of about $40\mathrm{G}/\mathrm{cm}$ is applied during the expansion for about 7 ms. (a)–(e) Along the entire evaporative cooling sequence, atoms are always spin-polarized in the lowest hyperfine sublevel $|F=19/2,m_F=-19/2⟩$. $T/T_F$ of the atomic samples are indicated in each panel. In (f), the image is obtained right after rf mixing of the spin states for the sample at $T/T_F=0.33(1)$. The three clouds correspond to the magnetic sublevels $m_F=-19/2$, $-17/2$, and $-15/2$ from bottom to top.

Figure 4

Effective elastic cross section as a function of $T/T_F$ after thermalization. In the nondegenerate regime, the effective cross section is constant and gives a mean value of $2.0(5)\times {10}^{-12}{\mathrm{cm}}^2$. The error bars for each point contain the statistical uncertainties of the time constant for cross-dimensional thermalization, of the trap frequencies, and of the temperature. A typical cross-dimensional thermalization measurement with an exponential fit to the data is shown in the inset. $T_z$ is the temperature along the $z$ direction.