Geometric quantum phase from the interaction of the permanent electric dipole moment of a neutral particle with an axial magnetic field

We study the appearance of a geometric quantum phase from the interaction of the permanent electric dipole moment of a neutral particle with an axial magnetic field produced by a nonuniform electric current density. We show that this geometric phase is a non-Abelian phase and a non-dispersive phase. We also show that it differs from the He-McKellar-Wilkens geometric quantum phase. Further, we consider the radial magnetic field produced by a nonuniform magnetization inside a long ferromagnetic wire, and thus, obtain the geometric quantum phase from the interaction of the electric dipole moment with the axial and radial magnetic fields. Then, we discuss the quantum holonomy which can be obtained in this neutral particle system.