title: Microwave experiments simulating quantum search and directed transport in artificial graphene.
abstract: A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to √N, where N is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grover's 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.
authors.affiliation: Laboratoire de Physique de la Matière Condensée, UMR 7336, Université Nice Sophia Antipolis, CNRS, Parc Valrose, 06100 Nice, France.
authors.forename: Julian
authors.initials: J
authors.lastname: Böhm
authors.affiliation: Laboratoire de Physique de la Matière Condensée, UMR 7336, Université Nice Sophia Antipolis, CNRS, Parc Valrose, 06100 Nice, France.
authors.forename: Matthieu
authors.initials: M
authors.lastname: Bellec
authors.affiliation: Laboratoire de Physique de la Matière Condensée, UMR 7336, Université Nice Sophia Antipolis, CNRS, Parc Valrose, 06100 Nice, France.
authors.forename: Fabrice
authors.initials: F
authors.lastname: Mortessagne
authors.affiliation: Laboratoire de Physique de la Matière Condensée, UMR 7336, Université Nice Sophia Antipolis, CNRS, Parc Valrose, 06100 Nice, France.
authors.forename: Ulrich
authors.initials: U
authors.lastname: Kuhl
authors.affiliation: AG Quantenchaos, Fachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany.|Applied Physics, University of Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany.
authors.forename: Sonja
authors.initials: S
authors.lastname: Barkhofen
authors.affiliation: AG Quantenchaos, Fachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany.|Department of Energy Management and Power System Operation, University of Kassel, D-34121 Kassel, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Gehler
authors.affiliation: AG Quantenchaos, Fachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany.
authors.forename: Hans-Jürgen
authors.initials: HJ
authors.lastname: Stöckmann
authors.affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Iain
authors.initials: I
authors.lastname: Foulger
authors.affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Sven
authors.initials: S
authors.lastname: Gnutzmann
authors.affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
authors.forename: Gregor
authors.initials: G
authors.lastname: Tanner