Efimov effect in $D$ spatial dimensions in $AAB$ systems

TL;DR

This paper investigates how the Efimov effect in $AAB$ systems depends on the spatial dimension $D$ and mass ratio, providing theoretical predictions for experimental verification in variable-dimensional setups.

Contribution

It determines the conditions for the Efimov effect to occur in $AAB$ systems across different dimensions and mass ratios, and predicts the discrete scaling factor for experimental tests.

Findings

Efimov effect exists only within specific dimensional ranges depending on mass ratio.

Derived the Efimov discrete scaling factor as a function of dimension and mass ratio.

Provided theoretical predictions testable with current experimental technology.

Abstract

The existence of the Efimov effect is drastically affected by the dimensionality of the space in which the system is embedded. The effective spatial dimension containing an atomic cloud can be continuously modified by compressing it in one or two directions. In the present article we determine for a general $AAB$ system formed by two identical bosons $A$ and a third particle $B$ in the two-body unitary limit, the dimensionsality $D$ for which the Efimov effect can exist for different values of the mass ratio $\mathpzc{A}=m_B/m_A$. In addition, we provide a prediction for the Efimov discrete scaling factor, ${\rm exp}\,(\pi/s)$, as a function of a wide range of values of $\mathpzc{A}$ and $D$, which can be tested in experiments that can be realized with currently available technology.