Electron spin states on a higher-order Bloch sphere

Based on the correspondence between the conventional Poincaré and Bloch spheres, we proposed a higher-order Bloch spheres, which is an extension of the conventional Bloch spheres. By calculating the expectation value of the spin components using the Pauli spin matrices, we found that the new spin state is formed in a ring shape and the orientation of the spin changes depending on the azimuthal angle and topological charge of orbital angular momentum. We also realize the coherent transfer of the azimuth-dependent polarization state of photons to the electron spin state in a GaAs quantum well with a V-shaped three-level system.