Laser systems and a linear radiofrequency (rf) Paul trap with an integrated co-axial cavity have been developed for experiments in cavity QED and probabilistic entanglement. Single 40Ca+ ions and large Coulomb crystals have been trapped routinely and laser cooled with long trapping lifetimes. A technique to achieve precise overlap of the pseudopotential minimum of the rf-field with the cavity mode has been implemented through variable capacitors in the resonant rf-circuit used to drive the trap. Three-dimensional micromotion compensation has been implemented. An 894 nm laser has been frequency stabilised to a Pound-Drever-Hall cavity which is in turn stabilised to atomic Cs using polarisation spectroscopy. The Allan variance of the error signal has been reduced to less than a kilohertz on timescales greater than a second. A novel implementation of the scanning cavity transfer lock has been developed to transfer the stability of the 894 nm laser to the 397 nm ion cooling and 866 nm repumping lasers. The bandwidth of the system has been increased to 380 Hz and the Allan variance of the error signal has been reduced to less than ten kilohertz on timescales of greater than a second. The pseudopotential minimum of the rf field has been overlapped optimally with the optical cavity mode through mapping of the fluorescence from cavity-field repumped ions as a function of their displacement. Coupling to the cavity mode has been confirmed by observation of resonant fluorescence into the cavity mode using the cavity-assisted Raman transition process. The thesis demonstrates that the setup is ready for the controlled production of single photons with pre-determined polarisation states, and progression onto new schemes to entangle multiple ions that are coupled to the optical cavity mode.

Entanglement is an established resource in quantum information processing, and there is a clear imperative to study many-body systems both in quantum technology applications and for probing fundamental physical laws. Ion trap cavity quantum electrodynamics is a highly promising platform for research. Prerequisites are the controlled coupling of many ions to the cavity field along with the ability to initialize the quantum states and drive coherent transitions between them. A coaxial ion trap and high finesse cavity system has been shown to couple strings of up to five ions to the cavity mode with nearly optimal coupling strength thanks to precise control over their positions in the standing wave and their mutual Coulomb interaction. The predictive power of the theoretical model demonstrates that the scheme can be extended to more ions or to higher coupling regimes. In a separate experiment it has been demonstrated that a quantum state can be initialized, before coherently transferring the population to a qubit state through the cavity interaction. The emission of polarized photons in the cavity mode has been measured, taking the system closer to the generation of cluster states for quantum information research and fundamental studies in many-body entanglement. Building on the aforementioned work, an infrastructure has been put in place for the direct observation of vacuum Rabi oscillations between a single ion and the cavity. In this scheme, the contribution to the dynamics from the dominant incoherent channel is minimized through post-selection of the data. As a quantum system coupled to a reservoir with memory, it will provide experimental constraints on theoretical work in the field of non-Markovian dynamics.

Over the past 15 years ion traps have demonstrated all the building blocks required of a quantum computer. Despite this success, trapping ions remains a challenging task, with the requirement for extensive laser systems and vacuum systems to perform operations on only a handful of qubits. To scale these proof of principle experiments into something that can outperform a classical computer requires an advancement in the trap technologies that will allow multiple trapping zones, junctions and utilize scalable fabrication technologies. I will discuss the construction of an ion trapping experiment, focussing on my work towards the laser stabilization and ion trap design but also covering the experimental setup as a whole. The vacuum system that I designed allows the mounting and testing of a variety of ion trap chips, with versatile optical access and a fast turn around time. I will also present the design and fabrication of a microfabricated Y junction and a 2- dimensional ion trap lattice. I achieve a suppression of barrier height and small variation of secular frequency through the Y junction, aiding to the junctions applicability to adiabatic shuttling operations. I also report the design and fabrication of a 2-D ion trap lattice. Such structures have been proposed as a means to implement quantum simulators and to my knowledge is the first microfabricated lattice trap. Electrical testing of the trap structures was undertaken to investigate the breakdown voltage of microfabricated structures with both static and radio frequency voltages. The results from these tests negate the concern over reduced rf voltage breakdown and in fact demonstrates breakdown voltages significantly above that typically required for ion trapping. This may allow ion traps to be designed to operate with higher voltages and greater ion-electrode separations, reducing anomalous heating. Lastly I present my work towards the implementation of magnetic fields gradients and microwaves on chip. This may allow coupling of the ions internal state to its motion using microwaves, thus reducing the requirements for the use of laser systems.

It is well known that quantisation of gravity within the conventional framework of quantum field theory faces challenges. An intriguing novel prospect was put forward by S. Weinberg in 1979 who suggested that the metric degrees of freedom of gravity could be quantised nonpertubatively provided that the theory becomes asymptotically safe (AS) at high energies. In this thesis we put forward a systematic search strategy to test the AS conjecture in four dimensional quantum gravity. Using modern renormalisation group (RG) methods and heat kernel techniques we derive the RG equations for gravitational actions that are formed from powers of the Ricci scalar and powers of the Ricci tensor. The non-linear fixed point equations are solved iteratively and exactly. We develop a sophisticated algorithm to express the fixed point iteratively, and to high order, in terms of its lower order couplings. We also evaluate universal scaling exponents and find that the relevancy of invariants at an asymptotically safe fixed point is governed by their classical mass dimension, providing structural support for the asymptotic safety conjecture. We also apply our findings to the physics of higher dimensional black holes. Most notably, we find that the seminal ultra-spinning Myers-Perry black holes cease to exist as soon as asymptotically safe RG corrections are taken into account. Further results and implications of our findings are discussed.

Microfabricated ion traps are an important tool in the development of scalable quantum systems. Tremendous advancements towards an ion quantum computer were made in the past decade and most requirements for a quantum computer have been fulfilled in individual experiments. Incorporating all essential capabilities in a fully scalable system will require the further advancement of established quantum information technologies and development of new trap fabrication techniques. In my thesis I will discuss the theoretical background and experimental setup required for the operation of ion traps. Measurement of the important ion trap heating rate was performed in the setup and I will discuss the results in more detail. I will give a review of microfabrication processes used for the fabrication of traps, outlining advantages, disadvantages and issues inherent to the processes. Following the review I will present my work on a concept for a scalable ion trap quantum system based on microwave quantum gates and shuttling through X-junctions. Many of the required building blocks, including ion trap structures with current-carrying wires intended to create strong magnetic field gradients for microwave gates were investigated further. A novel fabrication process was developed to combine current-carrying wires with advanced multilayered ion trap structures. Several trap designs intended for proof of principle experiments of high fidelity microwave gates, advanced detection techniques and shuttling between electrically disconnected ion traps will be presented. Also the electrode geometry of an optimized X-junction design with strongly suppressed rf barrier height will be presented. Further, I developed several modifications for the experimental setup to extend the existing capabilities. A plasma source capable of performing in-situ cleans of the trap electrode surfaces, which has been demonstrated to dramatically reduce the heating rate in ion traps, was incorporated. I will also present a vacuum system modification designed to cool ion traps with current-carrying wires and transport the generated heat out of the vacuum system. In addition a novel low-noise, high-speed, multichannel voltage control system was developed by me. The device can be used in future experiments to precisely shuttle ions from one trapping zone to another and also to shuttle ions through ion trap junctions. Lastly I will outline the process optimization and microfabrication of my ion trap designs. A novel fabrication process which makes use of the extremely high thermal conductivity of diamond substrates and combines it with thick copper tracks embedded in the substrate was developed. Large currents will be passed through the wires creating a strong and controllable magnetic field gradient. Ion trap designs with isolated electrodes connected via buried wires can be placed on top of the current-carrying wires, allowing the most advanced electrode designs to be fabricated with current-carrying wires.

Ions trapped in Paul traps provide a system which has been shown to exhibit most of the properties required to implement quantum information processing. In particular, a two-dimensional array of ions has been shown to be a candidate for the implementation of quantum simulations. Microfabricated surface geometries provide a widely used technology with which to create structures capable of trapping the required two-dimensional array of ions. To provide a system which can utilise the properties of trapped ions a greater understanding of the surface geometries which can trap ions in two-dimensional arrays would be advantageous, and allow quantum simulators to be fabricated and tested. In this thesis I will present the design, set-up and implementation of an experimental apparatus which can be used to trap ions in a variety of different traps. Particular focus will be put on the ability to apply radio-frequency voltages to these traps via helical resonators with high quality factors. A detailed design guide will be presented for the construction and operation of such a device at a desired resonant frequency whilst maximising the quality factor for a set of experimental constraints. Devices of this nature will provide greater filtering of noise on the rf voltages used to create the electric field which traps the ions which could lead to reduced heating in trapped ions. The ability to apply higher voltages with these devices could also provide deeper traps, longer ion lifetimes and more efficient cooling of trapped ions. In order to efficiently cool trapped ions certain transitions must be known to a required accuracy. In this thesis the 2S1/2 → 2P1/2 Doppler cooling and 2D3/2 → 2D[3/2]1/2 repumping transition wavelengths are presented with a greater accuracy then previous work. These transitions are given for the 170, 171, 172, 174 and 176 isotopes of Yb+. Two-dimensional arrays of ions trapped above a microfabricated surface geometry provide a technology which could enable quantum simulations to be performed allowing solutions to problems currently unobtainable with classical simulation. However, the spin-spin interactions used in the simulations between neighbouring ions are required to occur on a faster time-scale than any decoherence in the system. The time-scales of both the ion-ion interactions and decoherence are determined by the properties of the electric field formed by the surface geometry. This thesis will show how geometry variables can be used to optimise the ratio between the decoherence time and the interaction time whilst simultaneously maximising the homogeneity of the array properties. In particular, it will be shown how the edges of the geometry can be varied to provide the maximum homogeneity in the array and how the radii and separation of polygons comprising the surface geometry vary as a function of array size for optimised arrays. Estimates of the power dissipation in these geometries will be given based on a simple microfabrication.

Quantum field theories are considered fundamental provided they remain well-defined and predictive up to highest energies. Important such examples are known as asymptotic freedom and asymptotic safety where the high energy behaviour is controlled by a free or interacting fixed point under the renormalisation group, respectively. The focus of this thesis is the prospect of asymptotic safety for gauge theories and gravity. We are particularly interested in regimes where asymptotic safety arises at parametrically small coupling such as in large-N limits, where N relates to the degrees of freedom. Specifically, in the first part, we investigate exact ultraviolet (UV) fixed points of recently discovered four-dimensional gauge Yukawa theories in the Veneziano limit of SU(N) gauge theories coupled to matter. We include higher dimensional scalar self-interactions. Our main tools are perturbation theory in conjunction with non-perturbative \functional" renormalisation group (RG) techniques. It is established that classically irrelevant couplings take well-defined interacting fixed point values of their own, despite of their non-renormalisability within perturbation theory. We also establish vacuum stability, and show that higher order couplings remain parametrically irrelevant with near-Gaussian scaling exponents. Our results provide a crucial consistency check for exact asymptotic safety of weakly coupled gauge theories. Secondly, we perform a large-N study for quantum Einstein gravity. The main novelty here is that the number of space-time dimensions D takes the role of the number of degrees of freedom. We then derive and analyse renormalisation group equations within a 1/D expansion, also comparing the so-called single and bimetric approximations and the gauge-fixing dependence of results. In either of the cases we find an asymptotically safe gravitational fixed point and a finite radius of convergence in the 1/D expansion. We discuss the consistency of our results in comparison with previous findings, and in the light of the asymptotic safety conjecture for gravity in four dimensions.

The foundational theory of quantum enhanced metrology for parameter estimation is of fundamental importance to the progression of science and technology as the scientific method is built upon empirical evidence, the acquisition of which is entirely reliant on measurement. Quantum mechanical properties can be exploited to yield measurement results to a greater precision (lesser uncertainty) than that which is permitted by classical methods. This has been mathematically demonstrated by the derivation of theoretical bounds which place a fundamental limit on the uncertainty of a measurement. Furthermore, quantum metrology is of immediate interest in the application of quantum technologies since measurement plays a central role. This thesis focuses on the role of quantum correlations and uncertainty relations which govern the precision bounds. We show how correlations can be distributed amongst limited resources in realistic scenarios, as permitted by current experimental capabilities, to achieve higher precision measurements than current approaches. This is extended to the setting of multiparameter estimation in which we demonstrate a more technologically feasible method of correlation distribution than those previously posited which perform as well as, or worse than, our scheme. Furthermore, a quantum metrology protocol is typically comprised of three stages: probe state preparation, sensing and then readout, where the time required for the first and last stages is usually neglected. We consider the more realistic sensing scenario of time being a limited resource which is divided amongst the three stages and demonstrate the most efficient use of this resource. Additionally, we take an information theoretic approach to quantum mechanical uncertainty relations and derive a one-parameter class of uncertainty relations which supplies more information about the quantum mechanical system of interest than conventional uncertainty relations. Finally, we demonstrate how we can use this class of uncertainty relations to reconstruct information of the state of the quantum mechanical system.

Quantum technology has made great strides in the last two decades with trapped ions demonstrating all the necessary building blocks for a quantum computer. While these proof of principle experiments have been demonstrated, it still remains a challenging task to scale these experiments down to smaller systems. In this thesis I describe the development of technology towards scalable cryogenic ion trapping and quantum hybrid systems. I first discuss the fundamentals of ion trapping along with the demonstration of ion trapping on a novel surface electrode ion trap with a ring shaped architecture. I then present the development of a cryogenic vacuum system for ion trapping at ~4 K, which utilizes a closed cycle Gifford McMahon cryocooler with a helium gas buffered ultra-low vibration interface to mechanically decouple a ultra-high vacuum system. Ancillary technologies are also presented, including a novel in-vacuum superconducting rf resonator, low power dissipation ceramic based atomic source oven and an adaptable in-vacuum permanent magnet system for long-wavelength based quantum logic. The design and fabrication of microfabricated surface ion traps toward quantum hybrid technologies are then presented. A superconducting ion trap with an integrated high quality factor microwave cavity and vertical ion shuttling capabilities is described. The experimental demonstration of the cavity is also presented with quality factors of Q6~6000 and Q~15000 for superconducting niobium nitride and gold based cavities respectively, which are the highest demonstrated for microwave cavities integrated within ion trapping electrode architectures. An ion trap with a multipole electrode geometry is then presented, which is capable of trapping a large number of ions simultaneously. The homogeneity of five individual linear trapping regions are optimized and the design for the principle axis rotation of each linear region is presented. An overview of microfabrication techniques used for fabricating surface electrode ion traps is then presented. This includes the detailed microfabrication procedure for ion traps designed within this thesis. A scheme for the integration of ion trapping and superconducting qubit systems as a step towards the realization of a quantum hybrid system is then presented. This scheme addresses two key diffculties in realizing such a system; a combined microfabricated ion trap and superconducting qubit architecture, and the experimental infrastructure to facilitate both technologies. Solutions that can be immediately implemented using current technology are presented. Finally, as a step towards scalability and hybrid quantum systems, the interaction between a single ion and a microwaves field produced from an on chip microwave cavity is explored. The interaction is described for the high-Q microwave cavity designed in this thesis and a 171Yb+ion. A description of the observable transmission from the cavity is described and it is shown that the presence of a single ion can indeed be observed in the emission spectrum of high-Q microwave cavity even in the weak coupling regime.

Trapped ions are currently one of the most promising architectures for realising the quantum information processor. The long lived internal states are ideal for representing qubit states and, through controlled interactions with electromagnetic radiation, ions can be manipulated to execute coherent logic operations. In this thesis an experiment capable of trapping Yb+ ions, including 171Yb+, is presented. Since ion energy can limit the coherence of qubit manipulations, characterisation of an ion trap heating rate is vital. Using a trapped 174Yb+ ion a heating rate consistent with previous measurements of other ion species in similar ion traps is obtained. This result shows abnormal heating of Yb+ does not occur, further solidifying the suitability of this species for quantum information processing. Efficient creation, and cooling of trapped ions requires exact wavelengths for the ionising, cooling and repump transitions. A simple technique to measure the 1S0 ↔ 1P1 transition wavelengths, required for isotope selective photoionisation of neutral Yb, is developed. Using the technique new wavelengths, accurate to 60 MHz, are obtained and differ from previously published results by 660 MHz. Through a simple modification the technique can also predict Doppler shifted transition frequencies, which may be required in non-perpendicular atom-laser interactions. Using trapped ions, the 2S1=2 ↔ 2P1/2 Doppler cooling and 2D3/2 ↔ 2D[3/2]1/2 repump transitions are also measured to a greater accuracy than previously reported. Many experiments require wavelengths which can only be obtained using complex expensive laser systems. To remedy this a simple cost effective laser is developed to enable laser diodes to be operated at sub zero temperatures, extending the range of obtainable wavelengths. Additional diode modulation capabilities allow for the manipulation of atoms and ions with hyperfine structures. The laser is shown to be suitable for manipulating Yb+ ions by cooling a diode from 372 nm to 369 nm and simultaneously generating 2.1 GHz frequency sidebands. Coherent manipulation such as arbitrary qubit rotations, motional coupling and ground state cooling, are required for trapped ion quantum computing. Two photon stimulated Raman transitions are identified as a suitable technique to implement all of these requirements and an investigation into implementing this technique with 171Yb+ is conducted. The possibility of exciting a Raman transition via either a dipole or quadrupole transitions in 171Yb+ is analysed, with dipole transitions preferred because quadrupole transitions are found to be too demanding experimentally. An inexpensive setup, utilising a dipole transition, is designed and tested. Although currently limited the setup shows potential to be an inexpensive, high fidelity method of exciting a Raman transition.