Efimov effect for heteronuclear three-body systems at positive scattering length and finite temperature

We study the recombination process of three atoms scattering into an atom and diatomic molecule in heteronuclear mixtures of ultracold atomic gases with large and positive interspecies scattering length at finite temperature. We calculate the temperature dependence of the three-body recombination rates by extracting universal scaling functions that parametrize the energy dependence of the scattering matrix. We compare our results to experimental data for the ${}^{40}\mathrm{K}-{}^{87}\mathrm{Rb}$ mixture and make a prediction for ${}^6\mathrm{Li}-{}^{87}\mathrm{Rb}$. We find that contributions from higher partial wave channels significantly impact the total rate and, in systems with particularly large mass imbalance, can even obliterate the recombination minima associated with the Efimov effect.

Figure 1

The $S$-wave universal functions for ${}^{40}\mathrm{K}-{}^{87}\mathrm{Rb}, {}^{40}\mathrm{K}-{}^{133}\mathrm{Cs}, {}^6\mathrm{Li}-{}^{87}\mathrm{Rb}$, and ${}^6\mathrm{Li}-{}^{133}\mathrm{Cs}$.

Figure 2

Shown on the left is the $J=0$ recombination rate divided by the maximum threshold value $K_{\mathrm{th}}^{\max }$ for a variety of values of ${\theta }_{*0}$ in the ${}^{40}\mathrm{K}-{}^{87}\mathrm{Rb}$ system with ${\eta }_{*}=0.05$ and on the right is the $J=0$ recombination rate divided by the maximum threshold value $K_{\mathrm{th}}^{\max }$ for a variety of values of ${\theta }_{*0}$ in the ${}^6\mathrm{Li}-{}^{87}\mathrm{Rb}$ system with ${\eta }_{*}=0.2$.

Figure 3

Shown on the left is $K_3^{\left(J\right)}\left(E\right)/K_{\mathrm{th}}^{\max }$ for ${}^{40}\mathrm{K}-{}^{87}\mathrm{Rb}$ and on the right is $K_3^{\left(J\right)}\left(E\right)/K_{\mathrm{th}}^{\max }$ for ${}^6\mathrm{Li}-{}^{87}\mathrm{Rb}$.

Figure 4

Recombination rate constant ${\alpha }_T$ as a function of the scattering length $a$ for ${}^{40}\mathrm{K}-{}^{87}\mathrm{Rb}$ with ${\eta }_{*}=0.05\pm 0.02$ [20] and the three-body parameter adjusted to reproduce a recombination minimum at $a_{*0}\approx 5000a_0$. The dashed red line at $450\mathrm{nK}$ corresponds to the average temperature at which the data of Bloom et al. was taken [39].

Figure 5

Recombination rate constant ${\alpha }_T$ as a function of the scattering length $a$ for ${}^6\mathrm{Li}-{}^{87}\mathrm{Rb}$ for ${\eta }_{*}=0.2$ [26] with a recombination minimum at $a_{*0}\approx 610a_0$.

Figure 6

Shown on the left is the rate constant ${\alpha }_T\left(a\right)$ for ${}^{40}\mathrm{K}-{}^{133}\mathrm{Cs}$, with $a_{*0}=500a_0$ and ${\eta }_{*}=0.2$, and on the right is the rate constant ${\alpha }_T\left(a\right)$ for ${}^6\mathrm{Li}-{}^{133}\mathrm{Cs}$, with $a_{*0}=805a_0$ [40] and ${\eta }_{*}=0.2$.