Topological matter is an unconventional form of matter: it exhibits a global hidden order which is not associated to the spontaneous breaking of any symmetry. The defects of this exotic type of order are anyons, quasiparticles with fractional statistics. Except for the fractional quantum Hall effect, there is no experimental evidence as to the existence of topologically ordered phases and it remains a huge challenge to develop theoretical techniques to look for them in realistic models and find them in the laboratory. In this talk I will present different theoretical protocols which exploit the potential of ultracold atoms in optical lattices towards the artificial realization of topological order. Using superlattice architectures it is possible to create periodic arrays of plaquettes which can be manipulated in parallel. I will show how atoms in these plaquettes can be prepared in minimum versions of topologically ordered states, like Laughlin states, resonating valence bond states and string net condensates. Moreover, I will discuss a protocol to create and detect anyons in these minimum systems. Combining building block hamiltonians for each plaquette, I will then show how to artifitially drive the system into a topologically ordered state for the whole lattice.
A 348 Theresienst. 37