Three-body bound states of two bosons and one impurity in one dimension

TL;DR

This paper analyzes the bound states in a one-dimensional three-body system with two bosons and an impurity, revealing how mass ratios and three-body interactions influence the number and energies of bound states.

Contribution

It provides a complete phase diagram of three-body bound states across mass ratios and explores the effects of three-body interactions on state emergence.

Findings

Maximum of three bound states when impurity mass is large

Three-body interaction can induce additional bound states

Explicit wave functions and energies for bound states

Abstract

We investigate one-dimensional three-body systems composed of two identical bosons and one imbalanced atom (impurity) with two-body and three-body zero-range interactions. For the case in the absence of three-body interaction, we give a complete phase diagram of the number of three-body bound states in the whole region of mass ratio via the direct calculation of the Skornyakov-Ter-Martirosyan equations. We demonstrate that other low-lying three-body bound states emerge when the mass of the impurity particle is not equal to another two identical particles. We can obtain not only the binding energies but also the corresponding wave functions. When the mass of impurity atom is vary large, there are at most three three-body bound states. We then study the effect of three-body zero-range interaction and unveil that it can induces one more three-body bound state at a certain region of coupling strength ratio under a fixed mass ratio.