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 (n,1) 4 and E (n,2) 4, which are universally linked to the energy E 3 ) 1/2 ≈ 1.51 and (E (1,2) 4 /E3 ) 1/2 ≈ 1.01. The 133 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. PACS numbers:Continuous and discrete scale invariances underlie many phenomena in physics. The possibly most aesthetically appealing examples are fractals [1], where a given pattern repeats itself as one zooms in. Scale invariance phenomena also emerge in quantum mechanics. A prominent example is the three-body Efimov effect [2, 3]. If there exists an Efimov trimer of size l 3 . Here, λ (λ > 1) is a scaling factor that depends on the masses and particle statistics of the constituents.The experimental observation of consecutive threebody resonances is extremely challenging as it requires working in the universal Efimov window. To be in this window, the absolute values of at least two of the three two-body s-wave scattering lengths [5] have to be larger than the other length scales of the underlying two-body potentials and the temperature has to be lower than the energy scale set by the s-wave scattering length. Thus, to observe two consecutive three-atom resonances, exquisite control over the scattering lengths and ultralow temperatures are required. For three identical bosons, λ is approximately equal to 22.7 and two consecutive threeatom resonances in a bosonic system have only been observed recently in 133 Cs [6, 7].It is well known that the scaling factor λ takes smaller, and hence more favorable, values for heteronuclear mixtures with infinitely large interspecies s-wave scattering length [3,[8][9][10][11][12][13] [15] groups independently reported the experimental observation of, respectively, two and three consecutive Cs-Cs-Li three-atom resonances. The analysis shows that the Cs-Cs interactions play a negligible role at the present precision of the experiments, indicating that the observation of Efimov physics in these heavylight mixtures is due to the large magnitude of the Cs-Li s-wave scattering length.The extended Efimov scenario has been studied predominantly for four identical bosons with large in absolute value two-body s-wave scattering length [16][17][18][19][20][21][22]. In this case, there exist two four-body states with energies E (n,1) 4 and E (n,2) 4 that are universally tied to the nth Efimov trimer with energy E (n) 3 . These four-body states lead to measurable four-atom resonance...

Tetramer bound states in heteronuclear systems

“…[35]. A detailed study of the four-body states in a mixture of Cesium and Lithium atoms in the vicinity of the unitary limit and the three-atom threshold was recently performed by Blume and Yan [36]. For large enough mass ratios (M/m ≥ 16) they found two universal four-body states in the unitary limit.…”

“…We have chosen Gaussian potentials, because their matrix elements can be calculated analytically in the Gaussian Expansion Method (GEM). There are many prior calculations with Gaussian potentials [36,49], so we can easily validate our method.…”

“…The following columns give the ratios of the trimer ground state and E s and the ratio of the lowest two trimer states, respectively. [36] for the mass ratio M/m = 133/6. The numbers are taken from Fig.…”

“…1. The natural energy scale connected to the potential (13,14) is [36] for the mass ratio M/m = 133/6. The numbers are taken from Fig.…”

Visualizing the Efimov Correlation in Bose Polarons

“…Moreover, the diagrammatic approach we used in this work can be generalized to interacting boson systems, with the boson-boson interaction contributing to another scattering channel. Our method can also be systematically improved to include n-body correlations (n > 3) in a controllable matter, for instance, the effect of four-body bound states consisting of one 6 Li and three 133 Cs atoms [72], which may result in additional signals near the location of their appearances.…”