Thesis (Ph.D)--Physics, Georgia Institute of Technology, 2009. / Committee Chair: Michael Chapman; Committee Member: Alex Kuzmich; Committee Member: Brian Kennedy; Committee Member: Chandra Raman; Committee Member: Kenneth Brown. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Trapped-ion systems are a promising route toward the realization of both near-term and universal quantum computers. However, one of the pressing challenges is improving the fidelity of two-qubit entangling gates. These operations are often implemented by addressing individual ions with laser pulses using the M\o lmer-S\o rensen (MS) protocol. Amplitude modulation (AM) is a well-studied extension of this protocol, where the amplitude of the laser pulses is controlled as a function of time. We present an analytical study of AM using a Fourier series expansion so that the laser amplitude may be represented as a general continuous function. Varying the Fourier coefficients used to generate the pulse produces trade-offs between the laser power, gate time, and fidelity. We specifically study gate-timing errors, and we have shown that the sensitivity of the fidelity to these errors can be improved without a significant increase in the average laser power or the gate time. We plot atomic population vs. time for both the traditional MS protocol and the protocol with AM, highlighting the increased robustness of the AM gates. Our central result is that we improve the leading order dependence on gate timing errors from $\order{\Delta t^2}$ to $\order{\Delta t^6}$, and the protocol allows for arbitrarily high orders of scaling to be achieved in principle.

<p> Trapped ions can be isolated from external perturbations such as collisions with other atoms or electric and magnetic field inhomogeneities. For this reason, trapped ions can be useful in spectral measurements, quantum information technology and studying quantum behaviour. In this thesis, I discuss a trapped-Mg+ apparatus for studying the quantum mechanics of atoms. I describe the laser interactions that allow us to coherently excite our atoms. I go on to discuss the actual apparatus for trapping ions and making precise measurements, the hyperfine structure of 25 Mg+ and a proposed linewidth measurement. </p> / Thesis / Master of Science (MSc)

<P> Trapped ions are one of the best candidate systems to realize quantum computation. In our laboratory, we are trying to implement quantum computing and information processing: two hyperfine ground-states of magnesium-25 ions will serve as the two-level system to store quantum information. The ions are confined in a linear radio-frequency trap under ultra-high vacuum conditions and will be cooled down to their motional ground-states. By illuminating the ions with frequency-stabilized lasers we will be able to initialize, manipulate, and read out their internal electronic quantum states in a well-controlled way and with high fidelity. In addition, the ions can be made to interact with each other by coupling their internal electronic states to a collective vibrational mode of motion along the trap axis. In this thesis, the focus will be on the process of building a trapped-magnesium-ion quantum information processor. </p> / Thesis / Master of Science (MSc)

Application of precision laser spectroscopy and optical clock technology to the ground and metastable, first excited state of the ²²⁹Th nucleus at < 10 eV has significant potential for use in optical frequency metrology and tests of variation of fundamental constants. This work is a report on the development of required technologies to realize such a nuclear optical clock with a single, trapped, laser cooled ²²⁹Th³⁺ ion. Creation, trapping, laser cooling, and precision spectroscopy are developed and refined first with the naturally occurring isotope, ²³²Th. These technologies are then extended to laser cooling and precision laser spectroscopy of the electronic structure of ²²⁹Th³⁺. An efficient optical excitation search protocol to directly observe this transition via the electron bridge is proposed. The extraordinarily small systematic clock shifts are estimated and the likely extraordinarily large sensitivity of the clock to variation of the fine structure constant is discussed.

<p>Although trapped ion technology is well-suited for quantum information science, scalability of the system remains one of the main challenges. One of the challenges associated with scaling the ion trap quantum computer is the ability to individually manipulate the increasing number of qubits. Using micro-mirrors fabricated with micro-electromechanical systems (MEMS) technology, laser beams are focused on individual ions in a linear chain and steer the focal point in two dimensions. Multiple single qubit gates are demonstrated on trapped 171Yb+ qubits and the gate performance is characterized using quantum state tomography. The system features negligible crosstalk to neighboring ions (< 3e-4), and switching speeds comparable to typical single qubit gate times (< 2 us). In a separate experiment, photons scattered from the 171Yb+ ion are coupled into an optical fiber with 63% efficiency using a high numerical aperture lens (0.6 NA). The coupled photons are directed to superconducting nanowire single photon detectors (SNSPD), which provide a higher detector efficiency (69%) compared to traditional photomultiplier tubes (35%). The total system photon collection efficiency is increased from 2.2% to 3.4%, which allows for fast state detection of the qubit. For a detection beam intensity of 11 mW/cm2, the average detection time is 23.7 us with 99.885(7)% detection fidelity. The technologies demonstrated in this thesis can be integrated to form a single quantum register with all of the necessary resources to perform local gates as well as high fidelity readout and provide a photon link to other systems.</p> / Dissertation

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references. Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references. Available also in a digital version from Dissertation Abstracts.

Trapped atomic ions are one of the most promising systems for building a quantum computer -- all of the fundamental operations needed to build a quantum computer have been demonstrated in such systems. The challenge now is to understand and reduce the operation errors to below the 'fault-tolerant threshold' (the level below which quantum error correction works), and to scale up the current few-qubit experiments to many qubits. This thesis describes experimental work concentrated primarily on the first of these challenges. We demonstrate high-fidelity single-qubit and two-qubit (entangling) gates with errors at or below the fault-tolerant threshold. We also implement an entangling gate between two different species of ions, a tool which may be useful for certain scalable architectures. We study the speed/fidelity trade-off for a two-qubit phase gate implemented in ⁴³Ca^&plus; hyperfine trapped-ion qubits. We develop an error model which describes the fundamental and technical imperfections / limitations that contribute to the measured gate error. We characterize and minimise various error sources contributing to the measured fidelity, allowing us to account for errors due to the single-qubit operations and state readout (each at the 0.1&percnt; level), and to identify the leading sources of error in the two-qubit entangling operation. We achieve gate fidelities ranging between 97.1(2)&percnt; (for a gate time t_g = 3.8 &mu;s) and 99.9(1)&percnt; (for t_g = 100 &mu;s), representing respectively the fastest and lowest-error two-qubit gates reported between trapped-ion qubits by nearly an order of magnitude in each case. We also characterise single-qubit gates with average errors below 10^-4 per operation, over an order of magnitude better than previously achieved with laser-driven operations. Additionally, we present work on a mixed-species entangling gate. We entangle of a single ⁴⁰Ca^&plus; ion and a single ⁴³Ca^&plus; ion with a fidelity of 99.8(5)%, and perform full tomography of the resulting entangled state. We describe how this mixed-species gate mechanism could be used to entangle ⁴³Ca^&plus; and ⁸⁸Sr^&plus;, a promising combination of ions for future experiments.