Atom-dimer scattering for confined ultracold fermion gases

TL;DR

This paper investigates the three-body problem of ultracold Fermi gases under confinement, revealing universal atom-dimer interactions, resonance phenomena, and the absence of trimer states across different regimes.

Contribution

It provides a comprehensive analysis of atom-dimer scattering in confined ultracold Fermi gases, identifying universal behavior and characterizing interaction parameters across regimes.

Findings

Resonance at $a_ot/a \\approx 1.46$ on the two-body level

Universal atom-dimer scattering described by $a_{ad}$ and $b_{ad}$

No trimer states found in the system

Abstract

We solve the three-body problem of an ultracold Fermi gas with parabolic confinement length $a_\perp$ and 3D scattering length $a$. On the two-body level, there is a Feshbach-type resonance at $a_\perp/a\approx 1.46$, and a dimer state for arbitrary $a_\perp/a$. The three-body problem is shown to be universal, an d described by the atom-dimer scattering length $a_{ad}$ and a range parameter $b_{ad}$. In the dimer limit $a_\perp/a\gg 1$, we find a repulsive zero-range atom-dimer interaction. For $a_\perp/a\ll -1$, however, the potential has long range, with $a_{ad}>0$ and $b_{ad}\gg a_{ad}$. There is no trimer state, and despite $a_{ad}=0$ at $a_\perp/a\approx 2.6$, there is no resonance enhancement of the interaction.