Effective magnetic fields in ultracold atomic gases

We consider the influence of two resonant laser beams (to be referred to as the control and probe beams) on the mechanical properties of a degenerate atomic gas. The control and probe beams of light are assumed to have orbital angular momenta (OAM) and act on the three-level atoms in the electromagnetically induced transparency (EIT) configuration. We have carried out an explicit analysis of the quantum dynamics of the atom coupled with the two laser beams. Using the adiabatic approximation, we have obtained an effective equation of motion for the atoms driven to the dark state. The equation contains a vector potential type interaction as well as an effective trapping potential. The effective magnetic field is shown to be oriented along the propagation direction of the control and probe beams containing OAM. Its spatial profile can be controlled and shaped by choosing the proper laser beams. We have demonstrated how to generate a constant effective magnetic field both in the disc and ring geometrics of the atomic trap. We have also studied situations where the effective magnetic field exhibits a radial dependence. We have shown that the effective magnetic field can be concentrated within a region where the effective trapping potential holds the atoms. Furthermore the estimated magnetic length can be considerably smaller than the size of the atomic cloud.