Isotopic Shift of Atom-Dimer Efimov Resonances in K-Rb Mixtures: Critical Effect of Multichannel Feshbach Physics

Multichannel Efimov physics is investigated in ultracold heteronuclear admixtures of K and Rb atoms. We observe a shift in the scattering length where the first atom-dimer resonance appears in the ${}^{41}\mathrm{K}\text{−}{}^{87}\mathrm{Rb}$ system relative to the position of the previously observed atom-dimer resonance in the ${}^{40}\mathrm{K}\text{−}{}^{87}\mathrm{Rb}$ system. This shift is well explained by our calculations with a three-body model including van der Waals interactions, and, more importantly, multichannel spinor physics. With only minor differences in the atomic masses of the admixtures, the shift in the atom-dimer resonance positions can be cleanly ascribed to the isolated and overlapping Feshbach resonances in the ${}^{40}\mathrm{K}\text{−}{}^{87}\mathrm{Rb}$ and ${}^{41}\mathrm{K}\text{−}{}^{87}\mathrm{Rb}$ systems, respectively. Our study demonstrates the role of multichannel Feshbach physics in determining Efimov resonances in heteronuclear three-body systems.

Figure 1

Atom-dimer and dimer-dimer loss coefficients observed in an ultracold ${}^{41}\mathrm{K}\text{−}{}^{87}\mathrm{Rb}$ system. While the dimer-dimer (KRb-KRb) loss coefficient (open triangles) does not show any prominent features, the atom-dimer (Rb-KRb) loss coefficient (circles) shows a resonant feature. Lines of best fit for dimer-dimer and atom-dimer loss coefficients are illustrated by dashed and solid lines. The fit for the dimer-dimer loss coefficient assumes a linear dependence on $a$, while the fit for the atom-dimer loss assumes Eq. (2). The typical densities of the atoms and dimers are $n_{\mathrm{Rb}}=1.3\times 10^{11}$ and $n_{\mathrm{KRb}}=0.7\times 10^{11}{\mathrm{cm}}^{-3}$, respectively. The typical temperature is 60 nK.

Figure 2

The three-body recombination loss coefficient of the K-Rb-Rb collision in the vicinity of the heteronuclear Feshbach resonance (circles). The solid line shows an $a^4$ dependence, and the amplitude factor is determined by a fitting on the range of the positive scattering length $200a_0<a<1300a_0$. On the negative side, the amplitude factor is half of its value on the positive side [24].

Figure 3

Comparisons of numerically calculated and experimentally measured loss coefficients for (a) $\mathrm{Rb}+{}^{41}\mathrm{K}\mathrm{Rb}$ and (b) $\mathrm{Rb}+{}^{40}\mathrm{K}\mathrm{Rb}$ (experimental data obtained from Ref. [21]) collisions. In (a), the numerical results are multiplied by 5, which are thermally averaged at 20, 70, and 150 nK (dashed-dotted line, solid line, and dotted line). In (b), the numerical results are multiplied by 2, which are thermally averaged at 100, 300, and 500 nK (dashed-dotted line, solid line, and dotted line). In both graphs, results from numerical calculations at middle temperatures (shown in solid lines) show reasonable agreement with experimental results (shown in circles and triangles). The results from the fit using the effective field theory (dashed line) are also shown. The temperature of each measurement was $\sim 60$ (solid circles), $\sim 150$ (open triangles), and $\sim 300\mathrm{nK}$ (solid triangles), respectively.