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.

arXiv comment6 pages (2 figures) + 3 pages (3 figures)

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