# Long-lived trimers in a quasi-two-dimensional Fermi system

## TL;DR

This paper investigates three-body bound states (trimers) of three distinguishable fermions in a quasi-2D system, revealing how confinement affects Efimov trimers and suggesting potential for long-lived trimer states in ultracold gases.

## Contribution

It extends previous theoretical models by analyzing unequal two-body interactions and the evolution of trimers in quasi-2D, providing insights into their stability and spectrum.

## Key findings

- Deepest Efimov trimer remains unaffected by quasi-2D confinement.
- First excited trimer transitions from 3D Efimov to 2D-like state.
- Trimer lifetime can be increased by at least an order of magnitude in quasi-2D.

## Abstract

We consider the problem of three distinguishable fermions confined to a quasi-two-dimensional (quasi-2D) geometry, where there is a strong harmonic potential in one direction. We go beyond previous theoretical work and investigate the three-body bound states (trimers) for the case where the two-body short-range interactions between fermions are unequal. Using the scattering parameters from experiments on ultracold $^{6}$Li atoms, we calculate the trimer spectrum throughout the crossover from two to three dimensions. We find that the deepest Efimov trimer in the $^{6}$Li system is unaffected by realistic quasi-2D confinements, while the first excited trimer smoothly evolves from a 3D-like Efimov trimer to an extended 2D-like trimer as the attractive interactions are decreased. We furthermore compute the excited trimer wave function and quantify the stability of the trimer with respect to three-body recombination by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry, thus opening the door to realizing long-lived trimers in three-component Fermi gases.