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A Light-Matter Quantum Interface: Ion-Photon Entanglement and State Mapping

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A Light-Matter Quantum Interface: Ion-Photon Entanglement and State Mapping A light-matter quantum interface: ion-photon entanglement and state mapping Dissertation zur Erlangung des Doktorgrades an der Fakult¨atf¨urMathematik, Informatik und Physik der Leopold-Franzens-Universit¨atInnsbruck vorgelegt von Andreas Stute durchgef¨uhrtam Institut f¨urExperimentalphysik unter der Leitung von Univ.-Prof. Dr. Rainer Blatt Innsbruck, Dezember 2012 Abstract Quantum mechanics promises to have a great impact on computation. Motivated by the long-term vision of a universal quantum computer that speeds up certain calcula- tions, the field of quantum information processing has been growing steadily over the last decades. Although a variety of quantum systems consisting of a few qubits have been used to implement initial algorithms successfully, decoherence makes it difficult to scale up these systems. A powerful technique, however, could surpass any size limitation: the connection of individual quantum processors in a network. In a quantum network, “flying” qubits coherently transfer information between the stationary nodes of the network that store and process quantum information. Ideal candidates for the physical implementation of nodes are single atoms that exhibit long storage times; optical photons, which travel at the speed of light, are ideal information carriers. For coherent information transfer between atom and photon, a quantum interface has to couple the atom to a particular optical mode. This thesis reports on the implementation of a quantum interface by coupling a single trapped 40Ca+ ion to the mode of a high-finesse optical resonator. Single intra- cavity photons are generated in a vacuum-stimulated Raman process between two atomic states driven by a laser and the cavity vacuum field. In this Raman process, all Zeeman substates of the atom are spectroscopically resolved by tuning the frequency of the laser; via addressing specific atomic states, the polarization of the generated cavity photon is controlled, defining the photonic qubit. The electronic state of the ion is initialized, coherently manipulated, and read out via driving the quadrupole transition. With these techniques in hand, we have demonstrated two protocols for quantum communication. The first protocol, ion-photon entanglement, is regarded as a key resource of distributed quantum information processing. In our realization, we control both phase and amplitude of the entangled ion-photon state, resulting in a state fidelity of (97:4 ± 0:2)%. The second protocol, ion-photon state mapping, realizes a faithful transfer of the qubit state from the stationary to the flying qubit with a maximum process fidelity of (92 ± 2)%. The bichromatic driving scheme that we have developed enables time-independence of the quantum states in both protocols, making this scheme applicable to a variety of physical systems incorporating non-degenerate qubit states. In the future, the ion-photon interface that we have demonstrated will enable the coupling of distant ions; furthermore, it may allow for the optical coupling of an ion to other quantum systems, such as quantum dots or superconducting qubits. Such a hybrid quantum system could combine the advantages of the individual systems. Zusammenfassung Die Gesetze der Quantenmechanik versprechen, die Computertechnologie zu revo- lutionieren. Motiviert von der Vision eines universellen Quantencomputers ist das Forschungsfeld der Quanteninformationsverarbeitung in den letzten Jahrzehnten kon- tinuierlich gewachsen. Obwohl erste Algorithmen erfolgreich in kleinen Quantensyste- men mit einigen Quantenbits (Qubits) implementiert wurden, stellt die Skalierbarkeit dieser Systeme eine große Herausforderung dar. Hier k¨onnte eine bew¨ahrteTech- nik klassischer Computer helfen: Die Verbindung individueller Quantenprozessoren in einem Netzwerk. In einem solchen Quantennetzwerk ¨ubermitteln fliegende” Qubits koh¨arent Infor- " mation zwischen station¨arenKnotenpunkten des Netzwerkes, welche die Quanteninfor- mation speichern und verarbeiten. Ideal f¨urdie technische Realisierung der Knoten- punkte sind einzelne Atome, da sie lange Koh¨arenzzeiten besitzen. Als fliegende” " Qubits eignen sich optische Photonen, die in einer Glasfaser ¨ubertragen werden k¨onnen. F¨urden reversiblen Informationstransfer zwischen Atom und Photon wird eine Quan- tenschnittstelle ben¨otigt, welche das Atom gezielt an eine optische Mode koppelt. Die vorliegende Arbeit beschreibt die Realisierung einer solchen Schnittstelle, in der ein einzelnes 40Ca+ -Ion an die Mode eines optischen Resonators hoher G¨ute gekoppelt wird. Einzelne Photonen werden ¨uber einen Ramanprozess zwischen zwei atomaren Zust¨andenerzeugt. Dieser Ramanprozess wird vom Vakuumfeld des Res- onators und von einem Laser getrieben. Uber¨ die Frequenz des Lasers werden alle Zee- manzust¨andedes Atoms spektroskopisch aufgel¨ostund die Polarisation des erzeugten Photons kontrolliert. Die Polarisation des Photons definiert das fliegende” Qubit, " und der elektronische Zustand des Atoms definiert das station¨areQubit, welches ¨uber einen Quadrupol¨ubergang initialisiert, manipuliert und ausgelesen wird. Diese Techniken wurden anschließend angewendet, um zwei Protokolle f¨urdie Quantenkommunikation zu realisieren. Im ersten Protokoll wurde Atom-Photon- Verschr¨ankung erzeugt, die eine universelle Ressource f¨urdie Quantenkommunikation darstellt. In unserer Realisierung werden Phase und Amplitude des verschr¨ankten Atom-Photon-Zustandes mit einer Zustands-Fidelity von (97:4 ± 0:2)% kontrolliert. Im zweiten Protokoll wurde ein beliebiger Quantenzustand des Atoms koh¨arent auf das Photon ¨ubertragen. Hierbei betr¨agtdie maximale Prozess-Fidelity (92 ± 2)%. Das von uns entwickelte Anregungsschema mittels zweier phasenkoh¨arenter optischer Felder stellt die Zeitunabh¨angigkeit der Quantenzust¨andein beiden Protokollen sicher. Dieses Schema ist daher auf beliebige physikalische Systeme mit nichtentarteten Qub- itzust¨andenanwendbar. In Zukunft wird die hier realisierte Quantenschnittstelle die Kopplung entfern- ter Ionen sowie die Kopplung eines Ions an andere Quantensysteme wie Quanten- punkte oder supraleitende Qubits erm¨oglichen. Ein solches hybrides Quantensystem erm¨oglicht, die Vorteile der individuellen Systeme zu vereinen. Quand tu veux construire un bateau, ne commence pas par rassembler du bois, couper des planches et distribuer du travail, mais r´eveille au sein des hommes le d´esirde la mer grande et belle. Wenn du ein Schiff bauen willst, dann trommle nicht Menschen zusammen um Holz zu beschaffen, Aufgaben zu vergeben und die Arbeit einzuteilen, sondern lehre die Menschen die Sehnsucht nach dem weiten, endlosen Meer. Antoine de Saint-Exup´ery, Citadelle Contents 1 Introduction 1 2 Coupling an atomic qubit to a photon qubit 7 2.1 Quantum bits . .7 2.2 Two-level system coupled to a cavity . 12 2.3 Three-level system: vacuum-stimulated Raman transitions . 15 3 States and transitions in 40Ca+ for an ion-photon interface 19 3.1 Trapped calcium ions as quantum bits . 19 3.2 Transitions for generating single photons . 21 3.3 Model: Eighteen-level system coupled to two cavity modes . 22 4 Experimental setup 29 4.1 Overview . 29 4.2 Linear Paul trap . 31 4.3 Optical cavity . 32 4.4 Laser systems . 34 4.5 Transfer lock . 39 4.6 Laser beam geometry . 42 4.7 Ion addressing . 44 4.8 Magnetic field . 45 4.9 Atomic fluorescence detection . 47 4.10 Photon state detection . 47 4.11 Radiofrequency generation and data acquisition . 50 4.12 Technical considerations for a new setup . 51 5 Atomic qubit 53 5.1 Experimental sequence . 53 5.2 Doppler cooling . 53 5.3 State initialization . 56 5.4 State detection . 57 5.5 Coherent manipulation of the atomic qubit . 58 5.6 Sideband cooling . 59 5.7 Atomic coherence time: Ramsey spectroscopy . 61 5.8 Minimization of micromotion . 65 6 Controlling the ion-cavity coupling 69 6.1 Localization in the standing wave . 69 6.2 Probing the radial structure of the cavity mode . 70 7 Cavity-assisted Raman spectroscopy 75 7.1 Geometry of beams and magnetic field . 75 7.2 Raman spectra for different geometries . 79 7.3 Motional sidebands . 82 8 Tunable ion-photon entanglement 85 8.1 Motivation . 85 8.2 Entanglement and Bell inequalities . 86 8.3 Bichromatic Raman transition . 88 8.4 Experimental sequence and temporal pulse-shape overlap . 91 8.5 Quantum state tomography . 93 8.6 Time independence of the entangled state . 96 8.7 Tunable phase of the entangled state . 99 8.8 Tunable amplitudes of the entangled state . 99 8.9 Experimental imperfections . 101 8.10 Conclusion . 102 9 Ion-photon state mapping 105 9.1 Description of the protocol . 105 9.2 Implementation of the protocol . 105 9.3 Quantum process tomography . 108 9.4 Time evolution of the photon polarization . 109 9.5 Time independence of the mapping process . 112 9.6 Conclusion . 114 10 Summary and Outlook 115 A Battery circuit for trap-cavity piezo control 117 B Journal publications 119 Bibliography 131 Danksagung 133 1 Introduction Quantum mechanics represents one of the greatest advances in physics in the twen- tieth century. Not only does it explain fundamental phenomena in atomic physics, chemistry, material sciences, and many more areas of modern science, but also it has mediated the engineering of materials such as semiconductors, which resulted in the technical revolution of classical computation. In the last decades, it was discovered that certain principles of quantum mechanics promise to have a great impact on computation. While classical qubits are in state 0 or one, quantum bits (qubits) can be in a superposition
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