Strongly interacting isotopic Bose-Fermi mixture immersed in a Fermi sea

We have created a triply quantum-degenerate mixture of bosonic ${}^{41}\mathrm{K}$ and two fermionic species ${}^{40}\mathrm{K}$ and ${}^6\mathrm{Li}$. The boson is shown to be an efficient coolant for the two fermions, spurring hopes for the observation of fermionic superfluids with imbalanced masses. We observe multiple heteronuclear Feshbach resonances, in particular a wide $s$-wave resonance for the combination ${}^{41}\mathrm{K}$-${}^{40}\mathrm{K}$, opening up studies of strongly interacting isotopic Bose-Fermi mixtures. For large imbalance in the local densities of different species, we enter the polaronic regime of dressed impurities immersed in a bosonic or fermionic bath.

Figure 1

Schematic of the experimental setup. Two Zeeman slowers yield optimized atom flux for ${}^6\mathrm{Li}$ and K, allowing a no-compromise approach to simultaneous magneto-optical trapping of ${}^{41}\mathrm{K}$, ${}^{40}\mathrm{K}$, and ${}^6\mathrm{Li}$ in the main chamber. All species are subsequently loaded into an optically plugged magnetic trap (inset). rf evaporation of ${}^{41}\mathrm{K}$ sympathetically cools the fermionic species. The inset shows the trapping potential, essentially identical for all species, along the horizontal $y$ axis perpendicular to the plug beam.

Figure 2

(a)–(c) Absorption images of triply degenerate quantum gases of ${}^{41}\mathrm{K}$, ${}^{40}\mathrm{K}$, and ${}^6\mathrm{Li}$, imaged after 8.12 ms, 4.06 ms, and 1 ms time-of-flight from the magnetic trap, respectively. The final rf-knife frequency was 500 kHz above the 254.0 MHz hyperfine transition of ${}^{41}\mathrm{K}$. The white circles indicate the Fermi radius in time-of-flight $t$, $R_F=\sqrt{2E_F/m}t$. (d)–(f) Azimuthally averaged column density. Solid dots: Gaussian fit to the wings of the column density. Solid black and blue lines are Gaussian and Fermi-Dirac fits to the entire profile. The deviation of the Gaussian fit from the data is more pronounced for the more deeply degenerate ${}^6\mathrm{Li}$ at $T/T_F=0.16$ than for ${}^{40}\mathrm{K}$ at $T/T_F=0.51$. The arrows indicate the Fermi radii. The atom numbers for ${}^6\mathrm{Li}$, ${}^{41}\mathrm{K}$, and ${}^{40}\mathrm{K}$ are $1.6\times {10}^5$, $1.1\times {10}^5$, and $2.0\times {10}^5$, respectively.

Figure 3

Observation of Pauli pressure and Bose condensation in a triply quantum degenerate mixture. Shown is the normalized release energy $E/E_F$ of each cloud vs the normalized temperature $T/T_F$. Bose condensation of ${}^{41}\mathrm{K}$ occurs at $T_c/T_F=0.52$, causing a sudden reduction in release energy below $T_c$. For fermions, in contrast, the release energy saturates due to Pauli pressure. Solid circles: ${}^6\mathrm{Li}$; open circles: ${}^{40}\mathrm{K}$; solid squares: ${}^{41}\mathrm{K}$. Solid lines: theory for an interacting Bose gas and a noninteracting Fermi gas. Dashed line: Boltzmann gas. The inset shows the evolution of the phase space density (PSD) with atom number ($N$) during evaporation of ${}^{41}\mathrm{K}$. Open squares: Evaporation of ${}^{41}\mathrm{K}$ without ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$.

Figure 4

Observation of a wide Feshbach resonance in the isotopic Bose-Fermi mixture of ${}^{41}\mathrm{K}$-${}^{40}\mathrm{K}$. (a) The atom loss feature vs magnetic field is centered at $B_0=542.7\pm 0.5$ G. (b) Absorption images of the Bose and Fermi clouds after time of flight. The ${}^{40}\mathrm{K}$ image was scaled by the ratio of expansion factors of the Bose and Fermi cloud, the images thus approximately illustrate the in-trap density distribution. The white rim indicates the Fermi radius. (c) and (d) Atom number and reduced temperature $T/T_F$ vs wait time at the Feshbach resonance. Circles: ${}^{40}\mathrm{K}$; squares: ${}^{41}\mathrm{K}$. Dashed line: Bose-Einstein Condensate threshold $T_c/T_F=0.52$.