Two-Element Mixture of Bose and Fermi Superfluids

We report on the production of a stable mixture of bosonic and fermionic superfluids composed of the elements ${}^{174}\mathrm{Yb}$ and ${}^6\mathrm{Li}$ which feature a strong mismatch in mass and distinct electronic properties. We demonstrate elastic coupling between the superfluids by observing the shift in dipole oscillation frequency of the bosonic component due to the presence of the fermions. The measured magnitude of the shift is consistent with a mean-field model and its direction determines the previously unknown sign of the interspecies scattering length to be positive. We also observe the exchange of angular momentum between the superfluids from the excitation of a scissors mode in the bosonic component through interspecies interactions. We explain this observation using an analytical model based on superfluid hydrodynamics.

Figure 1

(a) Gradient controlled forced evaporative cooling of a Li unitary Fermi gas. We image the atoms at 690 G with 2 ms TOF (scale bar is $100\mu \mathrm{m}$). Solid lines are bimodal fits to doubly integrated optical density (OD) profiles, with dashed lines indicating the thermal component. From top to bottom, the detected condensate fractions $f_c$ are 0, 0.2, 0.5, and $\ge 0.85$. (b) Yb BEC of $1.1\times 10^5$ (30 ms TOF) atoms coexisting with a Li superfluid of $0.8\times 10^5$ atoms. Solid line is a fit to a pure Thomas-Fermi BEC profile. Gravity is in the vertical direction for all images in (a) and (b). (c) Calculated in-trap fermionic (dashed red lines) and bosonic (solid blue line) superfluid density profiles for (upper panel) the combined superfluid lifetime measurement at unitarity and (lower panel) the bosonic dipole oscillation measurements at 780 G presented in Fig. 2. For the fermion we use the zero-temperature EOS $n_F({\mu }_F,a_F)$ and the local density approximation to obtain $n_F(\overrightarrow{r})$ [18, 30], and for the boson a pure BEC profile in the Thomas-Fermi limit. The gradient of $B^{\prime }=41\mathrm{G}/\mathrm{cm}$ ensures complete overlap of the two clouds, while $B^{\prime }=68\mathrm{G}/\mathrm{cm}$ guarantees $y_{0,B}=y_{0,F}$.

Figure 2

Yb BEC dipole oscillations without (blue circles, upper panel) and with (red circles, lower panel) the Li superfluid at 780 G. Center-of-mass position measured at 30 ms TOF (solid lines are fits, see text).

Figure 3

(a) While executing dipole oscillations along $\widehat{y}$, the tilt angle of the Yb BEC ${\theta }_B$ exhibits a modulation due to interactions with the horizontally offset Li superfluid. This in-trap angle modulation maps proportionally to a tilt ${\theta }_{B,\mathrm{TOF}}$ for long TOF. In the absorption image, the red axes are aligned to the major and minor axes of the BEC tilted 1.3° clockwise with respect to the trap eigenaxes (black). (b) Tilt angle measurements in the absence of Li. (c) and (d) Observation of a scissors mode excitation in Yb due to interaction with Li at 780 G ($1/k_F{a}_F=0.39$) and 720 G ($1/k_F{a}_F=1.2$).