Thermalization and Sub-Poissonian Density Fluctuations in a Degenerate Molecular Fermi Gas

We observe thermalization in the production of a degenerate Fermi gas of polar ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ molecules. By measuring the atom-dimer elastic scattering cross section near the Feshbach resonance, we show that Feshbach molecules rapidly reach thermal equilibrium with both parent atomic species. Equilibrium is essentially maintained through coherent transfer to the ground state. Sub-Poissonian density fluctuations in Feshbach and ground-state molecules are measured, giving an independent characterization of degeneracy and directly probing the molecular Fermi-Dirac distribution.

Figure 1

Upper panel: example oscillations of ${\mathrm{KRb}}^{*}$ at $B=546.1\mathrm{G}$, varying the overlap density $\overline{n}$. The values of $|a_{\mathrm{ad}}|=684(110)a_0$ and $648(88)a_0$ extracted from the middle and bottom data, respectively, are in good agreement. Lower panel: $|a_{\mathrm{ad}}|$ vs $B-B_0$. Dashed line is a fit to the experimental data; see main text. For comparison, the K-Rb scattering length $a(B)$ is shown (solid line). The overlap density for these measurements is $\overline{n}=1.0(1)\times {10}^{12}{\mathrm{cm}}^{-3}$. Vertical error bars denote the standard error; horizontal error bars reflect a small settling of $B$ during the hold time.

Figure 2

KRb $T/T_F$ vs Feshbach ramp rate. Error bars denote the standard error. The most degenerate molecules are created with intermediate ramp rates of $0.5–3\mathrm{G}/\mathrm{ms}$.

Figure 3

Variance vs mean number for nondegenerate K (open squares) and degenerate KRb (solid triangles), averaged over bins with similar mean number. The dashed line indicates equal mean and variance, the expected result for classical particles, and the solid curve is a guide to the eye.

Figure 4

(a) Mean (open symbols) and variance (solid symbols) profiles, in units of maximum particle number per bin, for K, ${\mathrm{KRb}}^{*}$, and KRb, averaged over the central 30 camera pixels of each image in the $z$ direction. Solid lines are fits of the mean and variance to the Fermi-Dirac distribution and Eq. (1), respectively, used to independently determine the $T/T_F$ of each set of images. (b) Comparison between $T/T_F$ extracted from both fitting methods for K (square), ${\mathrm{KRb}}^{*}$ (circle), and KRb (triangle). Dashed line indicates equal $T/T_F$ between the two methods. In both panels, KRb variance is not corrected for STIRAP effects (see main text). Error bars are statistical and correspond to standard errors of the mean.