Line of Dirac monopoles embedded in a Bose-Einstein condensate

The gauge field of a uniform line of magnetic monopoles is created using a single Laguerre-Gauss laser mode and a gradient in the physical magnetic field. We study the effect of these monopoles on a Bose condensed atomic gas, whose vortex structure transforms when more than six monopoles are trapped within the cloud. Finally, we study this transition with the collective modes.

Figure 1

(a) Geometry of the proposed scheme. Copropagating laser beams with winding numbers $\pm \ell$ and the physical magnetic field $\mathbf{B}$ are aligned along $z$. (b) The gauge field realized, with the line of monopoles in orange, the effective magnetic field as green arrows, and the atomic cloud as the blue sphere. (c) The level diagram for the three electronic ground states displaced by the external physical magnetic field $\mathbf{B}$. The irradiating laser beams $+\ell$ and $-\ell$ induce resonant coupling. In practice $\Delta \gg \delta$. (d) The relative axial $B_z$ to radial magnetic field $B_{\rho }$. The dashed green line denotes the path of constant radius in the trap, and the blue sheet is $B_z/B_{\rho }=0$.

Figure 2

The particle density isosurfaces of BECs containing (a) $N=4$, (b) $N=12$, (c) $N=55$ monopoles for the gauge field of the proposed setup. The isosurfaces for the artificial situation of a perfect line of (d) $N=4$, (e) $N=12$, and (f) $N=55$ monopoles. The brightness denotes the depth of the site on the $y$ axis. The right-hand plots of (a,b) view the condensate along the $z$ axis, and use the hue to display the condensate phase.

Figure 3

Flux $\Phi$ exiting the cloud as a function of the number of embedded monopoles $N$. The red (+) line shows the flux exiting radially, the blue ($\times$) line the flux exiting along the Dirac string. The grey shading denotes the region where the escaping flux is necessarily less than the monopolar charge contained. The vertical black line shows the theoretically predicted crossover when flux first exits away from the string.

Figure 4

Collective mode frequencies renormalized by the trapping potential ${\Omega }_{\lambda }/\omega$ as a function of number of embedded monopoles $N$ for different interaction strengths and trapping potentials. The dashed arrows highlight the expected modes in the $N=0$ and $N\to \infty$ limits.