  Recently, an effective non-Abelian magnetic field with a topology of a
monopole was shown to emerge from the adiabatic motion of multilevel atoms in
spatially varying laser fields [J. Ruseckas et al., Phys. Rev. Lett. 95, 010404
(2005)]. We study this monopole in a Bose-Einstein condensate (BEC) of
degenerate dressed states and find that the topological charge of the
pseudospin cancels the monopole charge resulting in a vanishing gauge invariant
charge. As a function of the laser wavelength, different stationary states are
classified in terms of their effect to the monopole part of the magnetic field
and a cross-over to vortex ground state is observed.
