Non-Abelian Magnetic Monopole in a Bose-Einstein Condensate

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 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 crossover to vortex ground state is observed.

Figure 1

Left panel: Mean field energies corresponding to the solutions of the Gross-Pitaevskii equation. States with $Q_S^{(1)}=\pm 1$ are practically indistinguishable in the plot. Right panel: Isosurfaces of the particle densities for (a) $k{a}_{\mathrm{ho}}=0.86$, (b) $k{a}_{\mathrm{ho}}=2.6$, (c) $k{a}_{\mathrm{ho}}=5.0$, and (d) $k{a}_{\mathrm{ho}}=6.3$. The corresponding points are marked with ● in the energy diagram. In (d), the ground state has a vortex. The particle density increases from dark (blue) to light (green) color.