# Tetramer Bound States in Heteronuclear Systems

## TL;DR

This paper investigates the universal spectrum of trimer and tetramer states in heteronuclear ultracold atom mixtures near the heavy-light dimer threshold, revealing how mass ratios influence their energy thresholds and potential for exotic state observation.

## Contribution

It provides a detailed calculation of the universal trimer and tetramer spectra in heteronuclear systems with varying mass ratios using the Gaussian expansion method.

## Key findings

- Trimer and tetramer thresholds nearly coincide at certain mass ratios.
- As the mass ratio decreases, thresholds for these states become closer.
- Discussion of potential observation of exotic dimer-atom states.

## Abstract

We calculate the universal spectrum of trimer and tetramer states in heteronuclear mixtures of ultracold atoms with different masses in the vicinity of the heavy-light dimer threshold. To extract the energies, we solve the three- and four-body problem for simple two- and three-body potentials tuned to the universal region using the Gaussian expansion method. We focus on the case of one light particle of mass $m$ and two or three heavy bosons of mass $M$ with resonant heavy-light interactions. We find that trimer and tetramer cross into the heavy-light dimer threshold at almost the same point and that as the mass ratio $M/m$ decreases, the distance between the thresholds for trimer and tetramer states becomes smaller. We also comment on the possibility of observing exotic three-body states consisting of a dimer and two atoms in this region and compare with previous work.