Artificial Magnetic Fields in Momentum Space in Spin-Orbit Coupled Systems

TL;DR

This paper explores how Berry curvature creates effective magnetic fields in momentum space for spin-orbit coupled systems, revealing novel phenomena and potential experimental applications in ultracold gases and photonics.

Contribution

It introduces a framework to interpret momentum space as a magnetic system using effective Hamiltonians for spin-orbit coupled particles.

Findings

Momentum space can be modeled as a Fock-Darwin Hamiltonian or a ring with magnetic flux.

Identifies magnetic phenomena analogous to real-space effects in momentum space.

Discusses extensions to higher spin systems and experimental realizations.

Abstract

The Berry curvature is a geometrical property of an energy band which can act as a momentum space magnetic field in the effective Hamiltonian of a wide range of systems. We apply the effective Hamiltonian to a spin-1/2 particle in two dimensions with spin-orbit coupling, a Zeeman field and an additional harmonic trap. Depending on the parameter regime, we show how this system can be described in momentum space as either a Fock-Darwin Hamiltonian or a one-dimensional ring pierced by a magnetic flux. With this perspective, we interpret important single-particle properties, and identify analogue magnetic phenomena in momentum space. Finally we discuss the extension of this work to higher spin systems, as well as experimental applications in ultracold atomic gases and photonic systems.