Crossover from a Molecular Bose-Einstein Condensate to a Degenerate Fermi Gas

We demonstrate a reversible conversion of a ${}^6\mathrm{Li}_2$ molecular Bose-Einstein condensate to a degenerate Fermi gas of atoms by adiabatically crossing a Feshbach resonance. By optical in situ imaging, we observe a smooth change of the cloud size in the crossover regime. On the Feshbach resonance, the ensemble is strongly interacting and the measured cloud size is $75(7)\%$ of the one of a noninteracting zero-temperature Fermi gas. The high condensate fraction of more than $90\%$ and the adiabatic crossover suggest our Fermi gas to be cold enough to form a superfluid.

Figure 1

Axial density profiles of a partially condensed (a) and fully condensed (b) molecular cloud. The profiles are derived from averaging seven in situ images taken at a magnetic field of $B=676\mathrm{G}$ after evaporation at the production field of 764 G. (a) When the evaporation ramp is stopped with $4\times {10}^5$ molecules at a final laser power of 28 mW, a characteristic bimodal distribution is observed with a condensate fraction of $\sim 20\%$. The dashed curve shows Gaussian fit to the thermal fraction. (b) At a final laser power of 3.8 mW, an essentially pure condensate of $2\times {10}^5$ molecules is obtained.

Figure 2

Axial profile of a molecular BEC at 764 G (●) after its conversion into a Fermi gas at 1176 G and subsequent back conversion. Two 1-s magnetic field ramps are applied in this reversible process. For reference we show the corresponding profile observed without the magnetic field ramp (∘). The density profiles are obtained by averaging over 50 images. The difference shown in the lower graph is consistent with the drifts of a residual interference pattern in the images.

Figure 3

Axial cloud size measurements across the Feshbach resonance. In (a) the atomic scattering length $a$ is shown according to 17; the resonance at 850 G is marked by the vertical dashed line. The data in (b) display the measured rms cloud sizes. In (c), the same data are plotted after normalization to a noninteracting Fermi gas. The solid line shows the expectation from BEC mean-field theory with $a_{\mathrm{mol}}=0.6a$. In (b) and (c), the error bars show the statistical error of the size measurements from typically five individual images.

Figure 4

Observed axial density profiles near the Feshbach resonance, averaged over 50 images and symmetrized to reduce imaging imperfections. The rms cloud sizes are 93, 99, and $103\mu \mathrm{m}$ at $B=809$, 850, and 882 G, respectively. For comparison, the on-resonance data at 850 G are shown together with a fit by the expected profile $\propto (1-z^2/z_{\mathrm{TF}}^2{)}^{5/2}$. The small deviation near the top is due to a residual interference pattern in the images.