In this thesis is presented the realisation of 'The Geonium Chip', a novel planar Penning trap. The chip is designed with the goal of building a truly scalable planar Penning trap, while retaining the accuracy of 3D traps. Manufactured with conventional metalon- silicon microfabrication techniques, the chip takes the 5 electrodes of the compensated cylindrical trap and projects them onto a ground-plane surface, thus forming the basis for its layout by reducing the electrode shape to an array of at rectangular surfaces. In this thesis I describe the conception, design and construction of a full cryogenic set-up, including the magnetics, for trapping and observing a single electron in the Geonium Chip Penning trap. The cyclotron mode of the trapped electron lies in the microwave regime, and thus the Geonium Chip has the potential to become a powerful building block for quantum microwave circuits, with coherent coupling to the cyclotron degree of freedom. This will also allow non-destructive measurement and interaction with the spin state of the electron. The development of the experimental process is detailed from scratch including the design, fabrication, and testing of the Geonium Chip, as well as the design, fabrication and testing of the experimental apparatus. The original solutions and space saving designs developed as part of the construction process are detailed, such as the custom on-chip cryogenic vacuum chamber, planar magnetic field source, and the LED-based electron loading system. The vacuum chamber and control systems are also described, and the in-house manufacturing capabilities of the Geonium group are detailed at length, with an emphasis on rapid prototyping high-accuracy components suitable for experimental use. The apparatus built within this PhD is within a few weeks of performing the first loading of electrons into the chip trap.

Quantum electrodynamics is the spectacularly successful theory of the interaction of light and matter. Its consequences are well-understood, and have been experimentally verified to extreme precision. What is not generally known is how these predictions change when the theory is considered in anything other than free space - near a surface, for example. A material boundary causes vacuum fluctuations of the electromagnetic field to be different from their counterparts in free space, causing the electromagnetic environment of a microscopic system sitting near the boundary to differ from that if the surface were not present. This causes a variety of surface-dependent shifts in the properties of the microscopic system - this work investigates these shifts for a free electron. First using explicit normal mode expansion and analytic continuation of the wave-vector in the complex plane, and then using a semi-phenomenological `noise current' approach, the work presents derivations of formulae for the shifts in the mass and magnetic moment of an electron near a dispersive and absorbing surface. The formalism is also extended to the case where the electron is subject to a harmonic potential. It is noted that results for different models of the surface do not agree in the expected limiting cases due to their differing behaviour at low frequency, which leads to the conclusion that one must be very careful to use an appropriate model of a particular surface when considering quantum electrodynamic surface effects. Analysis of the results shows that use of a realistic model of the surface can make these shifts orders of magnitude larger than previous calculations had suggested, since they all relied on the somewhat unrealistic assumption that the surface is perfectly reflecting. This is shown to be particularly relevant to experiments which aim to measure the anomalous magnetic moment of an electron.

In this work, I detail the reconstruction and upgrades performed on the axial cavity ion trap in the ITCM group at the university of Sussex, and the measurement of the coupling of multiple ions to the cavity mode. This enables the optimal coupling between the ions and the cavity by adjusting the ions position in the radial and axial positions. This covers new ground in extending the optimal coupling beyond two ions which is of great importance for experiments with several ions in an optical cavity. The thesis outlines the background theory of light-matter interaction and cavity QED, before describing the physical ion trap hardware and its assembly. A description of the laser and cavity systems is provided, including techniques for locking both to stable references. A number of novel measurement techniques for measuring and maximising the stability of the ions and cavities are presented, including micromotion minimisation, spectroscopy, magnetic field compensation using the ground state Hanle effect, and Raman spectroscopy. These techniques enable the measurement of crucial parameters of the atomic transitions and the cavity. The work culminates in a description of the optimisation of the coupling between ion strings and the cavity first by adjusting the radial trap position by means of variable capacitors attached to RF electrodes, and then axially by means of adjusting the endcap potentials and therefore the spacing between ions to obtain the greatest localisation while still positioning the ions close to the antinodes of the cavity field.

Scalability is a challenging yet key aspect required for large scale quantum computing and simulation using ions trapped in radio-frequency (rf) Paul traps. In this thesis 171Yb+ ions are used to demonstrate a magnetic field insensitive qubit which has a measured coherence time of 1.5 s, making it an ideal candidate to use for storing quantum information. A magnetic field sensitive qubit is also characterised which can be used for the implementation of multi-qubit gates using a potentially very scalable scheme based on microwaves in conjunction with a static magnetic field gradient instead of using lasers. However, the measured coherence time is limited by magnetic field fluctuations and will prohibit high fidelity gate operations from being performed. To address this issue, the preparation of a dressed-state qubit using a microwave based stimulated rapid adiabatic passage (STIRAP) pulse sequence will be presented. This qubit is protected against the noisy environment making it less sensitive to magnetic field fluctuations. The lifetime of this qubit is measured to demonstrate its suitability for storing quantum information. A powerful method for manipulating the dressed-state qubit will be presented and is used to measure a coherence time of the qubit of 500 ms which is two orders of magnitude longer compared to the magnetic field sensitive qubit. It will also be shown that our method allows for the implementation of arbitrary rotations of the dressed-state qubit on the Bloch sphere using only a single rf field. This substantially simplifies the experimental setup for single and multi-qubit gates. Furthermore, this thesis will present a experimental setup capable of successfully operating microfabricated surface ion traps. This setup is then used to operate and characterise the first two-dimensional (2D) lattice of ion traps on a microchip. A unique feature of the microfabrication technique used for this device is the extremely large voltage that can be applied which allows long ion lifetimes along with large secular frequencies to be measured, demonstrating the robustness of this device. Rudimentary shuttling between neighbouring lattice sites will be shown which could be used as part of a efficient scheme to load a large lattice of ions. One of the many applications of a 2D lattice of ions lies in the field of quantum simulations where many-body systems such as quantum magnetism, high temperature superconductivity, the fractional quantum hall effect and synthetic gauge fields can be simulated. It will be shown how making only minor modifications to the microchip the ion-ion separation can be reduced sufficiently to offer an exciting platform for the successful implementation of 2D quantum simulations. A theoretical investigation on the optimal 2D ion trap lattice geometry will also be presented with the aim to maximise the ratio of ion-ion coupling strength to decoherence from motional heating of the ions and to laser induced off-resonant coupling.