Universality of Efimov states in mass-imbalanced cold atom mixtures with van der Waals and dipole interactions*

 Efimov state are 3-body bound states featuring discrete scale invariance that appear in a 3-body system interacting near s-wave unitarity[1]. The behavior of Efimov state is characterized by the 3-body parameter. For systems interacting via the van der Waals interaction, the 3-body parameter is universally determined by the van der Waals length regardless of atomic spices  or internal spin states.

Recently, some broad Feshbach resonances in the Er-Li mixture  have been observed experimentally[2]. As Er is much heavier than Li, this system is expected to exhibit fermionic Efimov states. Another important feature of this system is that Er have strong magnetic moment., so that the dipole interaction is as strong as the van der Waals interaction.,

To elucidate the role of the dipole interaction on the Efimov states, we theoretically investigated the 3-body parameter of the Efimov state  in the presence of van der Waals and dipole interactions [3].  By solving the Er-Er-Li(heavy-heavy-light) 3-body problem, we have found that the 3-body parameter still follows the van der Waals universality once the effect of the dipole interaction is renormalized into the s-wave and p-wave scattering parameters between the heavy particles. From this renormalized van der Waals universality and the analytical formulae obtained with the quantum defect theory, we estimate the 3-body parameters in the Er-Li system.  

[1] V. Efimov, Phys. Lett. B 33, 563 (1970).

[2] F. Schafer, Y. Haruna, and Y. Takahashi, J. Phys. Soc. Jpn. 92, 054301 (2023).  

[3] K. Oi, P. Naidon, S. Endo, Phys. Rev. A 110, 033305 (2024)