Trapping neutral particles endowed with a magnetic moment by an   electromagnetic wave carrying orbital angular momentum: Semiclassical theory
  The motion of a neutral atom endowed with a magnetic moment interacting with the magnetic field is determined from the Ehrenfest-like equations of motion. These equations for the average values of the translational and spin degrees of freedom are derived from the Schr\"odinger-Pauli wave equation and they form a set of nine coupled nonlinear evolution equations. The numerical and analytic solutions of these equations are obtained for the combination of the rotating magnetic field of a wave carrying orbital angular momentum and a static magnetic field. The running wave traps the atom only in the transverse direction while the standing wave traps the atom also in the direction of the beam. 
Iwo Bialynicki-Birula and Tomasz Rado\.zycki
physics.atom-ph quant-ph