Bound states of spin-orbit coupled cold atoms in a Dirac delta-function potential

TL;DR

This paper analyzes bound states of spin-orbit coupled cold atoms in a delta-function potential, revealing analytical solutions and phase characteristics, including stripe, separated, and zero-momentum phases, along with semi-bound states.

Contribution

It provides an analytical study of bound and semi-bound states in a spin-orbit coupled cold atom system with delta potential, highlighting phase features and evanescent mode properties.

Findings

Bound states exhibit stripe, separated, or zero-momentum phases.

Analytical solutions constructed from evanescent modes.

Properties of semi-bound states discussed.

Abstract

Dirac delta-function potential is widely studied in quantum mechanics because it usually can be exactly solved and at the same time is useful in modeling various physical systems. Here we study a system of delta-potential trapped spinorbit coupled cold atoms. The spin-orbit coupled atomic matter wave has two kinds of evanescent modes, one of which has pure imaginary wavevector and is an ordinary evanescent wave; while the other with a complex number wave vector is recognized as oscillating evanescent wave. We identified the eigenenergy spectra and the existence of bound states in this system. The bound states can be constructed analytically using the two kinds of evanescent modes and we found that they exhibit typical features of stripe phase, separated phase or zero-momentum phase. In addition to that, the properties of semi-bound states are also discussed, which is a localized wave packet on a plane wave background.