In this article, we revisit the heteronuclear Efimov effect in a Bose-Fermi mixture with large mass difference in the Born-Oppenheimer picture. As a specific example, we consider the combination of bosonic $^{133}\mathrm{Cs}$ and fermionic $^6\mathrm{Li}$. In a system consisting of two heavy bosons and one light fermion, the fermion-mediated potential between the two heavy bosons gives rise to an infinite series of three-body bound states. The intraspecies scattering length determines the three-body parameter and the scaling factor between consecutive Efimov states. In a second scenario, we replace the single fermion by an entire Fermi Sea at zero temperature. The emerging interaction potential for the two bosons exhibits long-range oscillations leading to a weakening of the binding and a breakup of the infinite series of Efimov states. In this scenario, the binding energies follow a modified Efimov scaling law incorporating the Fermi momentum. The scaling factor between deeply bound states is governed by the intraspecies interaction, analogous to the Efimov states in vacuum.

中文翻译：

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费米子遇到两个玻色子——重新审视异核埃菲莫夫效应

在本文中，我们重新审视了玻色-费米混合物中的异核 Efimov 效应，该混合物在 Born-Oppenheimer 图片中具有很大的质量差异。作为一个具体的例子，我们考虑玻色子 $^{133}\mathrm{Cs}$ 和费米子 $^6\mathrm{Li}$ 的组合。在由两个重玻色子和一个轻费米子组成的系统中，两个重玻色子之间的费米子介导势会产生无限系列的三体束缚态。种内散射长度决定了三体参数和连续 Efimov 状态之间的比例因子。在第二种情况下，我们在零温度下用整个费米海替换单个费米子。两个玻色子的新兴相互作用势表现出长程振荡，导致束缚减弱和 Efimov 状态的无限级数破裂。在这种情况下，结合能遵循包含费米动量的修改后的 Efimov 标度定律。深度束缚态之间的比例因子由种内相互作用控制，类似于真空中的 Efimov 态。