Relativistic Vortices in Bose-Einstein Condensates

We present two different approaches to the formation of vortices for a Bose-Einstein condensate in a honeycomb optical lattice. In the first approach, we consider vortices in the condensate order parameter. These are multi-component localized solutions of the nonlinear Dirac equation with nontrivial rotation about a core phase singularity. They are different from ordinary spinor vortices because the Berry phase induced by the lattice background supports a remarkable boson-fermion mapping in the quasi-particle operator statistics. Another type of vortex occurs when we add a mass gap by including distortions of both the nearest neighbor and next-nearest neighbor hopping, as well as a staggered chemical potential between the two sublattices. Vortices with fractional statistics emerge when the superfluid order parameter is integrated over a topological defect in the mass gap.

Funded by NSF.