The three-body pseudo-potential for atoms confined in one dimension

TL;DR

This paper derives a three-body pseudo-potential for atoms confined in one dimension, connecting zero-range potentials with the dimensional reduction of the three-body Schrödinger equation, relevant for ultracold atom experiments.

Contribution

It introduces a novel three-body pseudo-potential in one dimension and explores its implications using the Born approximation for ultracold atoms in a waveguide.

Findings

Derived the three-body pseudo-potential for 1D atoms

Connected zero-range potential with dimensional reduction near dimer threshold

Analyzed the Born approximation in the context of ultracold atoms

Abstract

Following a strong analogy with two-dimensional physics, the three-body pseudo-potential in one dimension is derived. The Born approximation is then considered in the context of ultracold atoms in a linear harmonic waveguide. In the vicinity of the dimer threshold a direct connection is made between the zero-range potential and the dimensional reduction of the three-body Schr{\"o}dinger equation.