title: Implementation of a quantum metamaterial using superconducting qubits.
abstract: The key issue for the implementation of a metamaterial is to demonstrate the existence of collective modes corresponding to coherent oscillations of the meta-atoms. Atoms of natural materials interact with electromagnetic fields as quantum two-level systems. Artificial quantum two-level systems can be made, for example, using superconducting nonlinear resonators cooled down to their ground state. Here we perform an experiment in which 20 of these quantum meta-atoms, so-called flux qubits, are embedded into a microwave resonator. We observe the dispersive shift of the resonator frequency imposed by the qubit metamaterial and the collective resonant coupling of eight qubits. The realized prototype represents a mesoscopic limit of naturally occurring spin ensembles and as such we demonstrate the AC-Zeeman shift of a resonant qubit ensemble. The studied system constitutes the implementation of a basic quantum metamaterial in the sense that many artificial atoms are coupled collectively to the quantized mode of a photon field.
authors.affiliation: 1] Leibniz Institute of Photonic Technology, PO Box 100239, D-07702 Jena, Germany [2] Physikalisches Institut, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany [3] ARC Centre for Engineered Quantum Systems, University of Queensland, Brisbane, Queensland 4072, Australia.
authors.forename: Pascal
authors.initials: P
authors.lastname: Macha
authors.affiliation: Leibniz Institute of Photonic Technology, PO Box 100239, D-07702 Jena, Germany.
authors.forename: Gregor
authors.initials: G
authors.lastname: Oelsner
authors.affiliation: 1] Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany [2] DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany.
authors.forename: Jan-Michael
authors.initials: JM
authors.lastname: Reiner
authors.affiliation: 1] Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany [2] DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Marthaler
authors.affiliation: 1] Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany [2] DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany.
authors.forename: Stephan
authors.initials: S
authors.lastname: André
authors.affiliation: 1] Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany [2] DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany.
authors.forename: Gerd
authors.initials: G
authors.lastname: Schön
authors.affiliation: Leibniz Institute of Photonic Technology, PO Box 100239, D-07702 Jena, Germany.
authors.forename: Uwe
authors.initials: U
authors.lastname: Hübner
authors.affiliation: Leibniz Institute of Photonic Technology, PO Box 100239, D-07702 Jena, Germany.
authors.forename: Hans-Georg
authors.initials: HG
authors.lastname: Meyer
authors.affiliation: 1] Leibniz Institute of Photonic Technology, PO Box 100239, D-07702 Jena, Germany [2] Russian Quantum Center, 100 Novaya Street, Skolkovo, Moscow region 143025, Russia.
authors.forename: Evgeni
authors.initials: E
authors.lastname: Il'ichev
authors.affiliation: 1] Physikalisches Institut, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany [2] Russian Quantum Center, 100 Novaya Street, Skolkovo, Moscow region 143025, Russia [3] National University of Science and Technology MISIS, Leninsky prosp. 4, Moscow 119049, Russia.
authors.forename: Alexey V
authors.initials: AV
authors.lastname: Ustinov