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arXiv:1410.2314 · Physical Review Letters

Generalized Efimov Scenario for Heavy-Light Mixtures

D. Blume, Yangqian Yan

Published Nov 18, 2014• 44 citations
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Abstract

Motivated by recent experimental investigations of Cs-Cs-Li Efimov resonances, this work theoretically investigates the few-body properties of $N\ensuremath{-}1$ noninteracting 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 $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ and vanishing $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ scattering lengths, we find $({E}_{4}^{(1,1)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.51$ and $({E}_{4}^{(1,2)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.01$. The $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ 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.

DOI
10.1103/physrevlett.113.213201

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Motivated by recent experiments on $^{6}\mathrm{Li}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ atomic mixtures with high mass imbalance, we study the Efimov correlation in an atomic system of two heavy bosons (133Cs^{133}\mathrm{Cs}133Cs) immersed in a bath of light fermions (6Li^{6}\mathrm{Li}6Li). Using the Born-Oppenheimer approximation, we identify two different regimes, depending on the Fermi momentum of light fermions (kF{k}_{F}kF​) and the boson-fermion scattering length as(<0){a}_{s}(<0)as​(<0), where the presence of an underlying Fermi sea plays distinct roles in the Efimov-type binding of bosons. Namely, in the regime ${k}_{F}|{a}_{s}|\ensuremath{\lesssim}1$ (${k}_{F}|{a}_{s}|\ensuremath{\gtrsim}1$), the Fermi sea induces an attractive (repulsive) effective interaction between bosons and thus favors (disfavors) the formation of a bound state, which can be seen as an Efimov trimer dressed by a fermion cloud. Interestingly, this implies nonmonotonic behavior of these bound states as increasing the fermion density (or kF{k}_{F}kF​). Moreover, we establish a generalized universal scaling law for the emergence and variation of such dressed Efimov bound states when incorporating a new scale (kF{k}_{F}kF​) brought on by the Fermi sea. These results can be directly tested in Li-Cs cold-atom experiments by measuring the modified bound-state spectrum and the shifted Efimov resonance, which manifest an emergent nontrivial Efimov correlation in a fermionic many-body environment.
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