Tests of Universal Three-Body Physics in an Ultracold Bose-Fermi Mixture

Recent measurements of Efimov resonances for a number of ultracold atom species have revealed an unexpected universality, in which three-body scattering properties are determined by the van der Waals length of the two-body interaction potential. To investigate whether this universality extends to heteronuclear mixtures, we measure loss rate coefficients in an ultracold trapped gas of ${}^{40}\mathrm{K}$ and ${}^{87}\mathrm{Rb}$ atoms. We find an Efimov-like resonance in the rate of inelastic collisions between ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ Feshbach molecules and ${}^{87}\mathrm{Rb}$ atoms. However, we do not observe any Efimov-related resonances in the rates of inelastic collisions between three atoms. These observations are compared to previous measurements by the LENS group of Efimov resonances in a ${}^{41}\mathrm{K}$ and ${}^{87}\mathrm{Rb}$ mixture as well as to recent predictions.

Figure 1

Measured $\beta$ vs $a$ for collisions of ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ molecules with ${}^{40}\mathrm{K}$ atoms in the $|9/2,-7/2⟩$ state (triangles), ${}^{40}\mathrm{K}$ atoms in the $|9/2,-9/2⟩$ state (squares), and ${}^{87}\mathrm{Rb}$ atoms in the $|1,1⟩$ state (solid diamonds). Vertical error bars indicate 1 standard deviation of statistical error, and horizontal error bars correspond to an upper bound of $\pm 0.02\mathrm{G}$ variation in $B$ across the cloud. A broad resonance is evident in the ${}^{87}\mathrm{Rb}+{}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ loss and the solid curve shows a fit to Eq. (2). A previous measurement of ${}^{87}\mathrm{Rb}+{}^{87}\mathrm{Rb}{}^{40}\mathrm{K}$ loss at lower temperature [29] (open diamonds) agrees well with our data, but did not cover the broad resonance. In plotting the previous data, we adjust $a$ to match a more recent calibration of the Feshbach resonance parameters that is used throughout the present work.

Figure 2

$\alpha$ vs $B$. There are two clear peaks near 546.6 G and 547.4 G: The first is the $s$-wave Feshbach resonance that we use to control $a$, and the second, much narrower feature we attribute to a $d$-wave interspecies Feshbach resonance. Vertical error bars show the statistical uncertainty in $\alpha$, and horizontal error bars show an upper bound of $\pm 0.03\mathrm{G}$ for the variation in $B$ during the measurement. Inset: $\alpha$ vs $B$ near the feature at 547.4 G. The solid, dotted, and dashed lines show the universal shape of an Efimov resonance, Eqs. (4, 5), for $\eta *=0.1$, $\eta *=0.02$, and $\eta *=0.004$.

Figure 3

Lower panel: $\alpha$ vs $a$. The error bars correspond to those in Fig. 2. The solid line shows an $a^4$ dependence with no Efimov resonances. To clarify the range of $a$ for which Efimov features are excluded, we include dashed and dash-dotted lines corresponding to universal Efimov resonance shapes located at $a_{-}=-200a_0$ and $a_{-}=-3000a_0$, respectively. Similarly, the dash-dot-dotted and dotted lines show hypothetical Efimov interference minima at $a_{+}=3000a_0$ and $a_{+}=200a_0$, respectively. A narrow two-body Feshbach resonance blocks experimental access to the range $-1090\le a/a_0\le -840$ (shaded rectangles on axes). Upper panel: The ratio of ${}^{87}\mathrm{Rb}$ loss to ${}^{40}\mathrm{K}$ loss vs $a$. The solid line shows $\Delta {\mathrm{N}}_{\mathrm{Rb}}/\Delta {\mathrm{N}}_{\mathrm{K}}=2$.