We report on experiments with strings of laser-cooled Ca+ ions for quantum information processing. An experiment using the isotope 43Ca+ was set up from scratch. We devised techniques for loading and laser-cooling 43Ca+ ion strings, initializing the ions in the hyperfine clock states and reading out the quantum state with high efficiency. Coherence times of the qubits are about 1 s. The single-qubit gates were implemented using microwave and Raman excitation, and coupling to the motional state was demonstrated. Very recently, a pair of 43Ca+ ions were entangled for the first time. In a second line of experiments, we demonstrated simple quantum algorithms with few 40Ca+ ions as well as the implementation of a high-fidelity gate operation entangling a pair of ions with a fidelity of 99.3(1)%. Among the milestone experiments are the demonstration and quantum process tomography of a Cirac-Zoller gate with mean fidelity of about 93%, the demonstration of entanglement in a decoherence-free sub space lasting for 20s, the demonstration of deterministic quantum teleportation, a Toffoli gate, deterministic entanglement swapping a partial measurement of a GHZ state preserving entanglement in the remaining qubits, creation and analysis of an 8-ion W-state, the application of entangled ions for precision spectroscopy.
We report on experiments with strings of laser-cooled Ca+ ions for quantum information processing. An experiment using the isotope 43Ca+ was set up from scratch. We devised techniques for loading and laser-cooling 43Ca+ ion strings, initializing the ions in the hyperfine clock states and reading out the quantum state with high efficiency. Coherence times of the qubits are about 1 s. The single-qubit gates were implemented using microwave and Raman excitation, and coupling to the motional state was demonstrated. Very recently, a pair of 43Ca+ ions were entangled for the first time. In a second line of experiments, we demonstrated simple quantum algorithms with few 40Ca+ ions as well as the implementation of a high-fidelity gate operation entangling a pair of ions with a fidelity of 99.3(1)%. Among the milestone experiments are the demonstration and quantum process tomography of a Cirac-Zoller gate with mean fidelity of about 93%, the demonstration of entanglement in a decoherence-free sub space lasting for 20s, the demonstration of deterministic quantum teleportation, a Toffoli gate, deterministic entanglement swapping a partial measurement of a GHZ state preserving entanglement in the remaining qubits, creation and analysis of an 8-ion W-state, the application of entangled ions for precision spectroscopy.
Over the last decade quantum information processing (QIP) has exploded into a major field of physics, studied both experimentally and theoretically with a universal quantum computer as a long-term vision. Ions stored as strings in linear Paul traps are among the most promising systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. The two most important challenges in trapped ion quantum computing today are to realize and control systems with large numbers of ions, and to improve and integrate the operations which serve as basic building blocks, in particular universal gate operations. Quite surprisingly, even after many years of intense research with different atom species, it is still not evident which ion is best suited for QIP. This thesis describes the construction of a new experiment built to study a promising candidate qubit, namely the calcium isotope 43Ca+. Due to its nuclear spin of I = 7/2, the isotope 43Ca+ exhibits a relatively complicated level structure, compared to other ions used so far for QIP. This work develops various strategies to successfully control such a complex level scheme. Initially we investigated the hyperfine structure of the 4s S1/2 ↔ 3d D5/2 quadrupole transition at a wavelength of 729 nm by laser spectroscopy using a single trapped 43Ca+ ion. We determined the hyperfine structure constants of the metastable level as AD5/2 = −3.893 12(3)MHz and BD5/2 = −4.239(1)MHz. The isotope shift of this transition with respect to 40Ca+ was measured to be ∆ iso /(2π) = 4 134 711 720(390)Hz. Armed with this knowledge, we were able to demonstrate ground-state cooling, robust state initialization and efficient readout of a qubit encoded in the ground-state hyperfine structure of a 43Ca+ ion. A microwave and a Raman light field were used to drive qubit transitions, and the coherence times for both fields were compared. Phase errors due to interferometric instabilities in the Raman field generation were not limiting the experiments on a time scale of at least 100ms. Even in the presence of magnetic field fluctuations we found a quantum information storage time exceeding one second. We implemented a Molmer-Sorensen type gate operation, entangling ions with a fidelity of 99.3(1)%. The gate was performed on a pair of qubits encoded in two trapped 40Ca+ ions using an amplitude-modulated laser beam interacting with both ions at the same time. A robust gate operation, mapping separable states onto maximally entangled states was achieved by adiabatically switching the laser-ion coupling on and off. The performance of a single gate and concatenations of up to 21 gate operations were analyzed. Concerning the fidelity, this result sets a world record for creating two-qubit entanglement on-demand irrespective of the physical realization considered. Zusammenfassung Die Quanteninformationsverarbeitung (QIV) als experimentelles und theoretisches Teilgebiet der Physik mit dem universellen Quantencomputer als Fernziel entwickelte sich innerhalb der letzten Dekade geradezu explosionsartig. Fur die technische Realisierung einer Maschine zur Ausnutzung der den Gesetzen der Quantenmechanik eigenen Rechenkraft gibt es eine Vielzahl an Moglichkeiten. Ionen, die sich in linearen Paul-Fallen wie auf einer Perlenschnur aufreihen, haben sich dabei mittlerweile als sehr vielversprechenden Ansatz etabliert. Die beiden grosten Herausforderungen der Ionenfallen-Experimente zur QIV bestehen gegenwartig in der Skalierung zu einer Vielzahl kontrollierter Quantenbits und in der Verbesserung und Integration der bereits demonstrierten Grundbausteine, insbesondere universeller Gatteroperationen. Uberraschenderweise ist auch nach vielen Jahren intensiver Forschung unklar, welche Ionen-Sorte zu diesem Zweck am besten geeignet ist. Die vorliegende Arbeit beschreibt den Aufbau eines neuen Experiments zur Untersuchung des Calciumisotops 43Ca+ als attraktiven Kandidaten. Aufgrund des Kernspins von I = 7/2 hat das Isotop 43Ca+, verglichen mit Atomsorten, die bisher fur die QIV verwandt wurden, ein komplizierteres Energieniveauschema. Diese Arbeit diskutiert die daraus resultierenden Moglichkeiten und beschreibt deren experimentelle Realisierung, so dass diese Komplexitat erfolgreich genutzt werden kann. Zunachst wurde die Hyperfein-Struktur des 4s S1/2 ↔ 3d D5/2 Quadrupol-Ubergangs bei einer Wellenlange von 729 nm mittels Laserspektroskopie an einem einzelnen 43Ca+Ion untersucht. Die Hyperfein-Konstanten des metastabilen Energieniveaus wurden zu AD5/2 = −3.893 12(3)MHz, BD5/2 = −4.239(1)MHz bestimmt. Als Nebenprodukt ergab sich die Isotopieverschiebung auf diesem Ubergang bezogen auf 40Ca+ zu ∆ iso /(2π) = 4 134 711 720(390)Hz. Mit diesem Wissen gelang es einzelne 43Ca+-Ionen nahe an den Bewegungsgrundzustand einer Mode zu kuhlen, sowie 43Ca+-Hyperfein-Qubits mit hoher Gute zu initialisieren und auszulesen. Die Koharenzzeiten dieses Hyperfein-Qubits wurden mit einem Mikrowellenfeld und einem Raman-Lichtfeld gemessen. Trotz der Anwesenheit magnetischer Storfelder konnte Quanteninformation uber eine Sekunde gespeichert werden. Auserdem ergaben Messungen, dass die interferometrischen Stabilitatsanforderungen der Raman-Lichtfelder, auf einer Zeitskala von 100ms keine Limitierung darstellen. Die Arbeit schliest mit der Beschreibung einer Molmer-Sorensen Gatteroperation, die verschrankte Zustande mit einer Gute von 99.3(1)% erzeugte. Dieser Gattertyp wurde erstmals auf einem optischen Qubit mittels eines amplitudenmodulierten Lasers realisiert, der an zwei 40Ca+-Ionen gleichermasen koppelte. Eine robuste Gatteroperation, die separable in verschrankte Zustande uberfuhrt, wurde durch adiabatisches Anund Ausschalten dieses Lasers erreicht. Zur Bestimmung moglicher Fehlerquellen wurden bis zu 21 aneinandergereihte Gatteroperationen analysiert. Bezuglich der erreichten Gute stellt das Ergebnis die momentan beste deterministische Zwei-Qubit-Verschrankungsoperation aller bekannter Systeme dar.
For quantum-information processing (QIP) with trapped ions, the isotope 43Ca+ offers the combined advantages of a quantum memory with long coherence time, a high-fidelity readout, and the possibility of performing two-qubit gates on a quadrupole transition with a narrow-band laser. Compared to other ions used for quantum computing, 43Ca+ has a relatively complicated level structure. We discuss how to meet the basic requirements for QIP and demonstrate ground-state cooling, robust state initialization, and efficient readout for the hyperfine qubit with a single 43Ca+ ion. A microwave field and a Raman light field are used to drive qubit transitions, and the coherence times for both fields are compared. Phase errors due to interferometric instabilities in the Raman field generation do not limit the experiments on a time scale of 100 ms. We find a quantum-information storage time of many seconds for the hyperfine qubit.
This thesis describes theoretical and experimental work whose main aim is the development of techniques for using trapped 43Ca⁺ ions for quantum information processing. I present a rate equations model of 43Ca⁺, and compare it with experimental data. The model is then used to investigate and optimise an electron-shelving readout method from a ground-level hyperfine qubit. The process is robust against common experimental imperfections. A shelving fidelity of up to 99.97% is theoretically possible, taking 100 μs. The laser pulse sequence can be greatly simplified for only a small reduction in the fidelity. The simplified method is tested experimentally with fidelities up to 99.8%. The shelving procedure could be applied to other commonly-used species of ion qubit. An entangling two-qubit quantum controlled-phase gate was attempted between a 40Ca⁺ and a 43Ca⁺ ion. The experiment did not succeed due to frequent decrystallisation of the ion pair, and strong motional decoherence. The source of the problems was never identified despite significant experimental effort, and the decision was made to suspend the experiments and continue them in an improved ion trap which is under construction. A sequence of pi-pulses, inspired by the Hahn spin-echo, was derived that is capable of greatly reducing dephasing of any qubit. If the qubit precession frequency varies with time as an nth-order polynomial, an (n+1) pulse sequence is theoretically capable of perfectly cancelling the resulting phase error. The sequence is used on a 43Ca+ magnetic-field-sensitive hyperfine qubit, with 20 pulses increasing the coherence time by a factor of 75 compared to an experiment without any spin-echo. In our ambient noise environment the well-known Carr-Purcell-Meiboom-Gill dynamic-decoupling method was found to be comparably effective.
Quantum information processing is performed with single trapped Ca(+) ions, stored in a linear Paul trap and laser-cooled to the ground state of their harmonic quantum motion. Composite laser-pulse sequences were used to implement SWAP gate, phase gate and controlled-NOT gate operations. Stark shifts on the quantum-bit transitions were precisely measured and compensated. For a demonstration of quantum information processing, a Deutsch-Jozsa algorithm has been implemented using two quantum bits encoded on a single ion.
Single ions in Paul traps are investigated for quantum information processing. Superpositions of the S1/2 and the D5/2 states are used to implement a qubit. The ions are optically cooled and fluorescence light at 397 nm on the S1/2-P1/2 transition is monitored for a state measurement by the “electron shelving” technique. The S1/2-D5/2 quadrupole transition at 729 nm is excited for sideband cooling and for quantum state preparation and manipulation. Individual ions in a linear string are addressed by a tightly focused 729 nm laser beam. A single Ca+ ion has been cooled in the spherical Paul trap to the ground state of vibration with up to 99.9% probability. Cooling is achieved in all three dimensions simultaneously as well as ground state cooling of two ions. Starting from a Fock state |n=0> coherent quantum state manipulation on the S1/2-D5/2 transition is achieved. The data show that decoherence is negligible on the time scale of a few oscillations, i.e. during the time required for a quantum gate operation. The measured several decoherence time of a few ms is attributed to residual laser and magnetic field fluctuations. Heating of the motional degrees of freedom has been measured directly and appears at a rate of 1 phonon per 190 ms (70 ms) at the secular frequencies ωaxial (ωradial). A novel type of ground state laser cooling of a single trapped ion is achieved using a technique which tailors the absorption profile for the cooling laser by exploiting electromagnetically induced transparency in the Zeeman structure of the S1/2–P1/2 dipole transition. This new method is robust, easy to implement and proves particularly useful for cooling several motional degrees of freedom simultaneously, which is of great practical importance for the implementation of quantum logic schemes with trapped ions.
The quest for a quantum system best satisfying the stringent requirements of a quantum information processor has made tremendous progress in many fields of physics. In the last decade, trapped ions have been established as one of the most promising architectures to accomplish the task. Internal states of an ion which can have extremely long coherence time can be used to store a quantum bit, and therefore allow many gate operations before the coherence is lost. Entanglement between multiple ions can be established via Coulomb interactions mediated by appropriate laser fields. Entangling schemes usually require the ions to be initialized to near their motional ground state. The interaction of fluctuating electric fields with the motional state of the ion leads to heating and thus to decoherence for entanglement generation limiting the fidelity of quantum logic gates. Effective ground state cooling of trapped ion motion and suppression of motional heating are thus crucial to many applications of trapped ions in quantum information science. In this thesis, I describe the implementation and study of several components of a Cadmium-ion-based quantum information processor, with special emphasis on the control and decoherence of trapped ion motion. I first discuss the building and design of various ion traps that were used in this work. I also report on the use of ultrafast laser pulses to photoionize and load cadmium ions in a variety of rf Paul trap geometries. A detailed analysis of the photoionization scheme is presented, along with its dependence on controlled experimental parameters. I then describe the implementation of Raman sideband cooling on a single trapped 111 Cd + ion to the ground state of motion, where a ground state population of 97% was achieved. The efficacy of this cooling technique is discussed with respect to different initial motional state distributions and its sensitivity to the presence of motional heating. I also present an experiment where the motion of a single trapped 112 Cd + ion is sympathetically cooled by directly Doppler cooling a 114 Cd + ion in the same trap. The implications of this result are relevant to the scaling of a trapped ion quantum computer, where the unwanted motion of an ion crystal can be quenched while not affecting the internal states of the qubit ions. (Abstract shortened by UMI.)