Stable Heteronuclear Few-Atom Bound States in Mixed Dimensions

TL;DR

This paper investigates stable few-body bound states in mixed-dimensional systems with heavy atoms in lower dimensions and a light atom in three dimensions, revealing novel Efimov-like states that are stable and exhibit resonant binding energies.

Contribution

It introduces the existence of stable three- and four-body bound states in mixed dimensions, extending Efimov physics to new geometries with geometric stability.

Findings

Existence of trimer and tetramer states in mixed dimensions.

Bound states persist at negative scattering lengths where no two-body bound states exist.

Maximum binding energy occurs when scattering lengths match trap separations.

Abstract

We study few-body problems in mixed dimensions with $N \ge 2$ heavy atoms trapped individually in parallel one-dimensional tubes or two-dimensional disks, and a single light atom travels freely in three dimensions. By using the Born-Oppenheimer approximation, we find three- and four-body bound states for a broad region of heavy-light atom scattering length combinations. Specifically, the existence of trimer and tetramer states persist to negative scattering lengths regime, where no two-body bound state is present. These few-body bound states are analogous to the Efimov states in three dimensions, but are stable against three-body recombination due to geometric separation. In addition, we find that the binding energy of the ground trimer and tetramer state reaches its maximum value when the scattering lengths are comparable to the separation between the low-dimensional traps. This resonant behavior is a unique feature for the few-body bound states in mixed dimensions.