Three-body problem for ultracold atoms in quasi-one-dimensional traps

TL;DR

This paper investigates the three-body interactions of ultracold atoms in quasi-one-dimensional traps, revealing universal and non-universal behaviors, and predicts a confinement-induced three-body bound state for bosons.

Contribution

It provides a comprehensive analysis of three-body problems for fermionic and bosonic cold atoms in quasi-1D traps, including exact results, numerical crossover, and the prediction of a new three-body bound state for bosons.

Findings

Fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths.

In the dimer limit, $b_{ad}=0$ and $a_{ad}$ relates to 3D scattering length.

A single confinement-induced three-body bound state (trimer) exists for bosons.

Abstract

We study the three-body problem for both fermionic and bosonic cold atom gases in a parabolic transverse trap of lengthscale $a_\perp$. For this quasi-one-dimensional (1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length $a$, and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths, $a_{ad}$ and $b_{ad}$. In the tightly bound `dimer limit', $a_\perp/a\to\infty$, we find $b_{ad}=0$, and $a_{ad}$ is linked to the 3D atom-dimer scattering length. In the weakly bound `BCS limit', $a_\perp/a\to-\infty$, a connection to the Bethe Ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is non-universal: $a_{ad}$ and $b_{ad}$ depend both on $a_\perp/a$ and on a parameter $R^*$ related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.