Three-body problem in a two-dimensional Fermi gas

TL;DR

This paper analyzes the three-body interactions in a two-dimensional Fermi gas, focusing on atom-dimer scattering, recombination rates, and bound states, revealing energy-dependent behaviors and trimer spectra akin to 2D hydrogen atoms.

Contribution

It provides exact calculations of atom-dimer scattering and three-body recombination in 2D Fermi gases, highlighting energy dependence and bound state spectra for different mass ratios.

Findings

Recombination rate is strongly energy dependent.

s-wave scattering described by scattering length for m_up < m_down.

Deeply bound trimers resemble 2D hydrogen atom spectra.

Abstract

We investigate the three-body properties of two identical "up" fermions and one distinguishable "down" atom interacting in a strongly confined two-dimensional geometry. We compute exactly the atom-dimer scattering properties and the three-body recombination rate as a function of collision energy and mass ratio m_up/m_down. We find that the recombination rate for fermions is strongly energy dependent, with significant contributions from higher partial waves at low energies. For m_up < m_down, the s-wave atom-dimer scattering below threshold is completely described by the scattering length. Furthermore, we examine the "up-up-down" bound states (trimers) appearing at large m_up/m_down and find that the energy spectrum for the deepest bound trimers resembles that of a hydrogen atom confined to two dimensions.