Figure 1: The accumulation of phase as a spin-$1/2$ particle moves through an inhomogeneous (quadrupole) magnetic field. The black vectors indicate the component of the normalized effective Zeeman field in the $e_x-e_y$ plane and the background color represents the $e_z$ component. The Bloch spheres show the enclosed solid angle, which sets the particle’s accumulated phase as it moves in a loop about the origin.