Artificial magnetic fields in momentum space in spin-orbit-coupled systems

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 analog 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.