Fermions meet two bosons -- the heteronuclear Efimov effect revisited

TL;DR

This paper revisits the heteronuclear Efimov effect in Bose-Fermi mixtures with large mass differences, analyzing how a Fermi Sea influences the formation and scaling of three-body bound states.

Contribution

It introduces a detailed analysis of Efimov states in Bose-Fermi mixtures, considering both single fermion and Fermi Sea scenarios, highlighting the effects on binding energies and scaling laws.

Findings

Fermion-mediated potential leads to infinite Efimov states in two heavy bosons and one light fermion.

Fermi Sea causes long-range oscillations, weakening binding and breaking the Efimov series.

Modified Efimov scaling law incorporates Fermi momentum, affecting state energies.

Abstract

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.