Generalized Efimov scenario for heavy-light mixtures

Abstract

Motivated by recent experimental investigations of Cs-Cs-Li Efimov resonances, this work theoretically investigates the few-body properties of $N-1$ non-interacting identical heavy bosons, which interact with a light impurity through a large $s$-wave scattering length. For Cs-Cs-Cs-Li, we predict the existence of universal four-body states with energies $E_4^{(n,1)}$ and $E_4^{(n,2)}$, which are universally linked to the energy $E_3^{(n)}$ of the $n$th Efimov trimer. For infinitely large $^{133}$Cs-$^6$Li and vanishing $^{133}$Cs-$^{133}$Cs scattering lengths, we find $(E_4^{(1,1)}/E_3^{(1)})^{1/2} \approx 1.51$ and $(E_4^{(1,2)}/E_3^{(1)})^{1/2} \approx 1.01$. The $^{133}$Cs-$^6$Li scattering lengths at which these states merge with the four-atom threshold, the dependence of these energy ratios on the mass ratio between the heavy and light atoms, and selected aspects of the generalized Efimov scenario for $N>4$ are also discussed. Possible implications of our results for ongoing cold atom experiments are presented.