Observation of Coupled Vortex Lattices in a Mass-Imbalance Bose and Fermi Superfluid Mixture

Quantized vortices play an essential role in diverse superfluid phenomena. In a Bose-Fermi superfluid mixture, especially of two mass-imbalance species, such macroscopic quantum phenomena are particularly rich due to the interplay between the Bose and Fermi superfluidity. However, generating a Bose-Fermi two-species superfluid, producing coupled vortex lattices within, and further probing interspecies interaction effects remain challenging. Here, we experimentally realize a two-species superfluid with dilute gases of lithium-6 and potassium-41, having a mass ratio of about seven. By rotating the superfluid mixture, we simultaneously produce coupled vortex lattices of the two species and thus present a definitive visual evidence for the double superfluidity. Moreover, we report several unconventional behaviors, due to the Bose-Fermi interaction, on the formation and decay of two-species vortices.

Figure 1

Sketch of experimental setup. An elliptical beam (light red) is superimposed with a Gaussian beam (blue) by a polarizing beam splitter (PBS), and then crossed with another elliptical beam (light red) at 90°. The dichromatic imaging beams are used for simultaneous absorption imaging of ${}^6\mathrm{Li}$ (green) and ${}^{41}\mathrm{K}$ (orange) atoms along the $z$ axis. The imaging beams after a beam splitter (BS) are respectively filtered by 671 nm and 767 nm bandpass filters, and then detected by the ${}^6\mathrm{Li}$ and ${}^{41}\mathrm{K}$ EMCCD cameras. An additional EMCCD camera is used for imaging the two species along the $x^{\prime }$ axis.

Figure 2

In situ images of two-species Bose-Fermi superfluid of ${}^{41}\mathrm{K}$ and ${}^6\mathrm{Li}$. The top and bottom row images, respectively, show the integrated optical density distributions of the two-species superfluid along the $x^{\prime }$ and $z$ directions, as the magnetic field is varied from the BEC to the BCS side of the ${}^6\mathrm{Li}$. The ${}^6\mathrm{Li}$ component has an inverse Fermi momentum of $1/k_F\approx 0.26\mu \mathrm{m}$. To take an in situ image, we prepare the superfluid mixture at 870 G, ramp the magnetic field to the desired value (from 762 G to 900 G) in 100 ms, and hold the trap for another 100 ms before imaging. Each picture is obtained by carefully superimposing two images that are taken separately in two experimental cycles (top) or simultaneously in a single cycle (bottom). It is seen that the ${}^{41}\mathrm{K}$ superfluid (bright region) is fully buried in the ${}^6\mathrm{Li}$ superfluid cloud. The viewing scope of top (bottom) images is $416\times 208\mu {\mathrm{m}}^2$ ($416\times 416\mu {\mathrm{m}}^2$).

Figure 3

Coupled vortex lattices in two-species superfluid. The top (bottom) images are for the ${}^6\mathrm{Li}$ (${}^{41}\mathrm{K}$) component, and the two images in each column, taken simultaneously in an experimental cycle, are for the same set of stirring parameters. (a),(d) are for separation $28\mu \mathrm{m}$, power 0.75 mW, rotating frequency 26 Hz; (b),(e) are for $52\mu \mathrm{m}$, 0.75 mW, 18 Hz; and (c),(f) are for $76\mu \mathrm{m}$, 1.5 mW, 22 Hz.

Figure 4

Comparison of vortex numbers in single- and two-species superfluids. For a given set of stirring parameters, three comparison experiments are respectively performed for the superfluid mixture and the single-species superfluid of ${}^6\mathrm{Li}$ or ${}^{41}\mathrm{K}$. Vortex numbers are counted and statistically averaged over 10 measurements with standard error margin being calculated. $2{\mathrm{SF}}_{\mathrm{Li}\text{−}\mathrm{K}}\text{−}\mathrm{Li}$ ($2{\mathrm{SF}}_{\mathrm{Li}\text{−}\mathrm{K}}\text{−}\mathrm{K}$) represents ${}^6\mathrm{Li}$ (${}^{41}\mathrm{K}$) component of two-species superfluid; SF-Li (SF-K) represents single species ${}^6\mathrm{Li}$ (${}^{41}\mathrm{K}$) superfluid. For each column of plots, the beam separation is fixed, while the rotating frequency is varied. Optimal frequencies for creating a maximal number of vortices are indicated by the filled (open) triangles on the horizontal axis with the same color of the data points. The interspecies interaction effects can be clearly seen from the dramatic difference of the ${}^6\mathrm{Li}$ vortex numbers (top row), over a wide range of rotating frequency.

Figure 5

Decay of vortices in single- and two-species superfluids. Three comparison experiments are carried out with the initial ${}^6\mathrm{Li}$ (${}^{41}\mathrm{K}$) vortex numbers being set approximately identical (see text). $2{\mathrm{SF}}_{\mathrm{Li}\text{−}\mathrm{K}}\text{−}\mathrm{Li}$ ($2{\mathrm{SF}}_{\mathrm{Li}\text{−}\mathrm{K}}\text{−}\mathrm{K}$) represents ${}^6\mathrm{Li}$ (${}^{41}\mathrm{K}$) component of two-species superfluid; SF-Li (SF-K) represents single species ${}^6\mathrm{Li}$ (${}^{41}\mathrm{K}$) superfluid. Each data point has a standard error bar and is gained by averaging over 10 measurements. The curves are obtained by fitting the experimental data to an exponential decay. The insets show typical images of vortices in the two-species superfluid, suggesting the survival of both ${}^6\mathrm{Li}$ and ${}^{41}\mathrm{K}$ vortices after 11 s.