Atom-dimer and dimer-dimer scatterings in a spin-orbit coupled Fermi gas

TL;DR

This paper investigates how spin-orbit coupling influences fermion-dimer and dimer-dimer scattering lengths in a three-dimensional Fermi gas, using diagrammatic methods and analyzing the validity of the Born approximation.

Contribution

It provides a detailed analysis of the effects of spin-orbit coupling on scattering lengths and benchmarks the Born approximation against higher-order corrections in different parameter regimes.

Findings

Born approximation is accurate when $1/(m \alpha a_s) \\ll -1$.

Higher-loop contributions are perturbative in the negative $1/(m \\alpha a_s)$ region.

All contributions become comparable in the positive $1/(m \\alpha a_s)$ region due to the growth of the dimer residue $Z$.

Abstract

Using the diagrammatic approach, here we study how spin-orbit coupling (SOC) affects the fermion-dimer and dimer-dimer scattering lengths in the Born approximation, and benchmark their accuracy with the higher-order approximations. We consider both isotropic and Rashba couplings in three dimensions, and show that the Born approximation gives accurate results in the $1/(m \alpha a_s) \ll -1$ limit, where $m$ is the mass of the fermions, $\alpha$ is the strength of the SOC, and $a_s$ is the $s$-wave scattering length between fermions. This is because the higher-loop contributions form a perturbative series in the $1/(m \alpha a_s) < 0$ region that is controlled by the smallness of the residue $Z$ of the dimer propagator. In sharp contrast, since $Z$ grows with the square-root of the binding energy of the dimer in the $1/(m \alpha a_s) > 0$ region, all of the higher-loop contributions are of similar order.