Energy spectra of two interacting fermions with spin-orbit coupling in a harmonic trap

TL;DR

This paper investigates the energy spectra of two spin-1/2 fermions in harmonic traps with various spin-orbit couplings, providing non-perturbative results relevant for experiments and adaptable to other systems.

Contribution

It introduces a non-perturbative method to analyze two-body spectra with different spin-orbit couplings in harmonic traps, applicable to both fermionic and bosonic systems.

Findings

Computed energy spectra for Rashba, Dresselhaus, and Weyl spin-orbit couplings.

Demonstrated the method's adaptability to different spin-orbit interactions.

Provided results relevant for experimental realizations of spin-orbit coupled systems.

Abstract

We explore the two-body spectra of spin-$1/2$ fermions in isotropic harmonic traps with external spin-orbit potentials and short range two-body interactions. Using a truncated basis of total angular momentum eigenstates, non-perturbative results are presented for experimentally realistic forms of the spin-orbit coupling: a pure Rashba coupling, Rashba and Dresselhaus couplings in equal parts, and a Weyl-type coupling. The technique is easily adapted to bosonic systems and other forms of spin-orbit coupling.