Generation and detection of matter-wave gap vortices in optical lattices

We analyze numerically the process of dynamical generation of spatially localized vortices in Bose-Einstein condensates (BEC's) with repulsive atomic interactions confined by two-dimensional optical lattices. Akin to bright solitons in a repulsive condensate, these nonlinear localized states exist only within the gaps of the matter-wave band-gap spectrum imposed by the periodicity of the lattice potential. We discuss the complex structure of matter-wave phase singularities associated with different types of stationary gap vortices and suggest two different excitation methods. In one method, the condensate is adiabatically driven to the edge of the Brillouin zone where a vortex phase is subsequently imprinted onto the condensate wave packet. Alternatively, a vortex is created in a condensate confined in a harmonic trap and then is nonadiabatically released into the lattice potential. We find that only the latter method leads to robust and reliable generation of vortices within the gap of the matter-wave band-gap spectrum. Moreover, the nonadiabatic excitation can lead to the formation of broad gap vortices from the initial BEC wave packets with a large number of atoms. These broad vortices are intimately connected to self-trapped nonlinear states of the BEC recently demonstrated in experiments with a one-dimensional optical lattice. Our numerical simulations also confirm the feasibility of a homodyne interferometric detection of broad gap vortices.