The Research Of Fractional Angular Momentum Realized By A Cold Atom

In this thesis,we propose several theoretical schemes to realize the fractional angular momentum(FAM)by using atoms which possess permanent magnetic,electric dipole moments and induced electric dipole moment.Firstly,we studied the way that obtains fractional angular momentum by using an atom which possesses permanent magnetic dipole moment interacting with electric fields.We showed that eigenvalues of the canonical angular momentum of the atom can be fractional when the atom is cooled down to its lowest kinetic energy level.The relationship between the canonical angular momentum and the kinetic angular momentum is also revealed.Then,we generalize this study to the noncommutative plane and find that there are two different mechanisms to realize the FAM.Secondly,we studied the interaction between an atom which possesses permanent electric dipole moment and magnetic fields.Our research showed that we can also obtain fractional angular momentum.The magnitude of the fractional part is determined by one of the electric field source densities and the magnetic dipole moment.Additionally,we realize the Chern-Simons quantum mechanics by this model simultaneously.Finally,we achieve fractional angular momentum by the atom which possesses an induced electric dipole moment.We analyze in detail the specific roles electromagnetic fields played in obtaining fractional angular momentum.