A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from $N$ to $sqrt{N}$, where $N$ is the number of items in the search space. In particular, devising searches on
regular lattices has become popular in extending Grovers original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses Dirac points. We present here a proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement. The idea is based on bringing localized search states into resonance with an extended lattice state in an energy region of low spectral density---namely, at or near the Dirac point. The experiment is implemented using classical waves in a microwave setup containing weakly coupled dielectric resonators placed in a honeycomb arrangement, i.e., artificial graphene. Furthermore, we investigate the scaling behavior experimentally using linear chains.
By means of a microwave tight-binding analogue experiment of a graphene-like lattice, we observe a topological transition between a phase with a point-like band gap characteristic of massless Dirac fermions and a gapped phase. By applying a controlle
d anisotropy on the structure, we investigate the transition directly via density of states measurements. The wave function associated with each eigenvalue is mapped and reveals new states at the Dirac point, localized on the armchair edges. We find that with increasing anisotropy, these new states are more and more localized at the edges.
Faithful communication is a necessary precondition for large scale all-optical networking and quantum information processing. Related theoretical investigations in different areas of physics have led to various proposals in which finite discrete latt
ices are used as channels for short-distance communication tasks. Here, in the framework of femtosecond-laser-written waveguide arrays, we present the first experimental realization of such a channel with judiciously engineered couplings.
