Fractionalized topological defects in optical lattices

Topological objects are interesting topics in various fields of physics ranging from condensed matter physics to the grand unified and superstring theories. Among those, ultracold atoms provide a playground to study the complex topological objects. In this paper we present a proposal to realize an optical lattice with stable fractionalized topological objects. In particular, we generate the fractionalized topological fluxes and fractionalized skyrmions on two-dimensional optical lattices and fractionalized monopoles on three-dimensional optical lattices. These results offer a new approach to study the quantum many-body systems on optical lattices of ultracold quantum gases with controllable topological defects, including dislocations, topological fluxes and monopoles.