  The regular structures obtained by optical lattice technology and their
behaviour are analysed from the quantum information perspective. Initially, we
demonstrate that a triangular optical lattice of two atomic species, bosonic or
fermionic, can be employed to generate a variety of novel spin-1/2 models that
include effective three-spin interactions. Such interactions can be employed to
simulate specific one or two dimensional physical systems that are of
particular interest for their condensed matter and entanglement properties. In
particular, connections between the scaling behaviour of entanglement and the
entanglement properties of closely spaced spins are drawn. Moreover, three-spin
interactions are well suited to support quantum computing without the need to
manipulate individual qubits. By employing Raman transitions or the interaction
of the atomic electric dipole moment with magnetic field gradients, one can
generate Hamiltonians that can be used for the physical implementation of
geometrical or topological objects. This work serves as a review article that
also includes many new results.
