Bound states of the spin-orbit coupled ultracold atom in a one-dimensional short-range potential

TL;DR

This paper investigates the bound states of a spin-orbit coupled ultracold atom in a one-dimensional short-range potential, revealing additional states induced by spin-orbit interaction that are not captured by traditional models.

Contribution

It demonstrates that point-interaction models of the potential can produce extra bound states due to spin-orbit coupling, expanding understanding of impurity effects in such systems.

Findings

Identification of spin-orbit induced bound states

Comparison of Fourier transform and eigenvalue methods

Extra states from point-interaction representations

Abstract

We solve the bound state problem for the Hamiltonian with the spin-orbit and the Raman coupling included. The Hamiltonian is perturbed by a one-dimensional short-range potential V which describes the impurity scattering. In addition to the bound states obtained by considering weak solutions through the Fourier transform or by solving the eigenvalue equation on a suitable domain directly, it is shown that ordinary point-interaction representations of V lead to spin-orbit induced extra states.