The eight-fold way for optical quasicrystals

In a recent paper we proposed a means to realize a quasicrystal with eight-fold symmetry by trapping particles in an optical potential created by four lasers. The quasicrystals obtained in this way, which are closely related to the well-known octagonal tiling, offer unique possibilities to study the effects of quasiperiodicity on physical properties. This method allows, furthermore, to transform the structures, to inflate or deflate them, include interactions or disorder and thus realize a large variety of theoretical models, both classical and quantum. In this paper we present details of the model, derive a number of interesting geometrical properties of the optical quasicrystals, as well as some results obtained by numerical calculations.