Higher-order Bloch spheres: A generalized representation of electron spin states with azimuthal phase factor

TL;DR

This paper introduces a generalized higher-order Bloch sphere framework to represent complex electron spin states with azimuthal phase factors, extending traditional models and analyzing their evolution in magnetic fields.

Contribution

It develops a higher-order Bloch sphere model for electron spins with azimuthal phase factors, linking photon polarization states to electron spin states and analyzing their dynamics.

Findings

Extended form of Larmor precession for higher-order spin states

Insights into coherent transfer between photon polarization and spin qubits

Potential applications in spin-orbital angular momentum systems

Abstract

Using the similarity between spin states on the Bloch sphere (BS) and polarization states on the Poincare sphere (PS), we construct higher-order spin states on the higher-order BS corresponding to higher-order polarization states of photons on the higher-order PS. We investigate the time evolution of higher-order spin states in a magnetic field and establish an extended form of the conventional Larmor precession. The results provide insights on coherent transfer from extended photons to extended spin qubit systems with spin and orbital angular momenta and the operation of extended spin qubits.