An elementary exposition of the Efimov Effect

TL;DR

This paper provides an elementary explanation of the Efimov effect, a quantum phenomenon where three particles form an infinite number of bound states, and summarizes recent experimental verification using ultra-cold atoms.

Contribution

It offers a simple, accessible derivation of the Efimov effect and its states, making the concept more understandable through elementary quantum mechanics.

Findings

Experimental verification with ultra-cold atoms

Elementary derivation of Efimov states

Summary of the effect's origin and implications

Abstract

Two particles that are just shy of binding may develop an infinite number of shallow bound states when a third particle is added. This counter intuitive quantum mechanical result was first predicted by V. Efimov for identical bosons interacting with a short-range pair-wise potential. The so-called Efimov effect persists even for non-identical particles, provided at least two of the three bonds are almost bound. The Efimov effect has recently been verified experimentally using ultra-cold atoms. In this article, we explain the origin of this effect using only elementary quantum mechanics, and summarize the experimental evidence for the Efimov effect. A new, simple derivation for the number of Efimov states is given in the Appendix.