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.

Cold atom traps are a promising tool for investigating and manipulating atomic behaviour. Radio frequency (RF) dressed cold atom traps allow high versatility of trapping potentials, which is important for potential applications, particularly in atom interferometry. This thesis investigates non-adiabatic spin flip transitions which can lead to losses of atoms from RF-dressed cold atom traps. We develop two models for the adiabatic potentials associated with RF-dressed traps, for the cases in which gravity does and doesn't have a significant effect. Within these two models we use first order perturbation theory to calculate decay rates for the number of dressed spin flip transitions per unit time. Our obtained decay rates are dependent on the atomic energy. For RF-dressed cold atom traps in which spin flip transitions lead to losses of atoms from the trap, we are able to predict ow non-adiabatic transitions decrease the trapped atom number. We achieve this by modelling the atomic distribution of energies for several different scenarios. The thesis concludes with a comparison to experimental data, including modelling how atomic energies are affected by noise in the currents generating the trapping magnetic fields.

Models with warped extra dimensions offer a promising solution to the hierarchy problem. However, it is known that flavour changing neutral currents arise at tree level in models with warped extra dimensions, which can lead to fatally large corrections to rare processes in the standard model. Since the introduction of the warped mechanism in 1999 by Randall and Sundrum, modifications of the original AdS5 geometries have been considered, having different phenomenologies. In particular, it has been previously shown that CP-violation in the K-K mixing system can be suppressed in what is known as the soft-wall model, in which the extra dimension is effectively compactified via a background scalar dilation field. Prior to the work presented in this thesis, however, this study had been limited to a background geometry with a specific form. A detailed study of bosonic propagators in soft-wall models has been conducted as part of this research, yielding some novel results, which permit the study of particle interactions throughout an extended family of warped 5D backgrounds in a practicable way. This methodology has then been applied, via the development of numerical routines, to an investigation of K and B meson phenomenology in a range of geometries in this family. The relevant and necessary technical prerequisites are reviewed and discussed, including (but not limited to) some of the general properties of warped extra dimensions, the application of Kaluza-Klein theory in warped 5D, topics in flavour physics and quark mixing and the application of effective field theory methods in perturbative calculations of flavour observables. It is found that there is indeed a significant interplay between the structure of the extra dimension and flavour phenomenology at a scale of 1-10 TeV. Although it turns out that the previously studied construction was already quite well-optimised with regard to flavour constraints, it is demonstrated that one can do more to ameliorate these via deformations to the background geometry and modifications to the power law dependence of the fermion masses on the extra dimension.

A quantum theory of gravity remains one of the greatest challenges of contemporary physics. It is well established that a perturbative treatment of gravity as a quantum field theory leads to a non-renormalisable setup. However gravity could still exist as a consistent and predictive quantum field theory on a non-perturbative level. This is explored in the asymptotic safety scenario which was initially proposed by S. Weinberg. In this thesis we investigate the ultraviolet behaviour of gravity within the asymptotic safety conjecture and discuss phenomenological implications. We start out by introducing the concept of the functional renormalisation group and its application to gravity. This non-perturbative tool is the technical basis for our investigation of a template quantum gravity action, namely a function f(R) in the Ricci scalar in four dimensions. We compute exact fixed point solutions to very high polynomial orders via the development of a dedicated high performance code. The picture of an interacting UV fixed point that receives only small quantitative corrections from higher derivative operators is confirmed and extended. The results are then expanded to include minimally coupled matter fields and we investigate the matter effects on the gravitational fixed point. We determine regimes of compatibility in the vicinity of the purely gravitational setup but also find constraints on the number of matter fields. Finally we look at the phenomenological implications of a running Newton's coupling, one of the key features of the asymptotic safety setup, to graviton-mediated eikonal scattering amplitudes. In this kinematic regime we investigate the possibility of a TeV-sized fundamental Planck mass via the introduction of compact extra dimensions. We identify the fingerprints of asymptotic safety in the t-channel scattering amplitude and find crucial differences compared to semi-classical computations.

The ATLAS experiment at the Large Hadron Collider has collected an unprecedented amount of data in the 3 years of data taking since its start. In this document I will discuss the results of the analysis I performed during my PhD at the university of Sussex for the search of Supersymmetry in events with three leptons (electron/muon/tau) and missing transverse energy in the final state. The search is performed on the full dataset collected by the experiment in 2012, at a centre-of-mass energy of 8 TeV. These results are interpreted in SUSY models with chargino-neutralino pair production via decays involving sleptons, staus, gauge bosons and the newly discovered Higgs boson. These results presented improve on previous searches performed at ATLAS in three lepton final states with only electrons and muons. Special focus will be given to the optimisation process of Supersymmetry signal with respect to the SM background, and the statistical interpretation of the results obtained with this search.

Positron emission tomography, or PET, is a medical imaging technique which has been used in clinical environments for over two decades. With the advent of fast timing detectors and scintillating crystals, it is possible to envisage improvements to the technique with the inclusion of time-of-flight capabilities. In this context, silicon photomultipliers coupled to fast inorganic LYSO crystals are investigated as a possible technology choice. As part of the ENVISION collaboration a range of photon detectors were investigated experimentally, leading to the selection of specific devices for use in a first prototype detector, currently being commissioned at the Rutherford Appleton Laboratory. In order to characterise the design of the prototype a GEANT4 simulation has been developed describing coupled systems of silicon photomultipliers and LYSO scintillators. Very good agreement is seen between the timing response of the experimental and simulated systems. Results of the simulation for a range of detector array arrangements are presented and a number of optimisations proposed for the final prototype design. Without the results provided here a detector system including only 3x3x5 mm3 crystals would have been adopted. A 3x3x5 mm3 crystal geometry is shown to provide little-to-no timing advantage over an identical system with 3x3x10 mm3 crystals, where detection efficiency is improved by approximately a factor of three. Additionally an investigation is presented which explores the impact of using events where gamma-ray photons are scattered internally within the detector array. It is shown that including such events could increase the signal achievable with one-to-one coupled detector arrays systems for PET by approximately 60%, with only minor reductions in coincidence timing resolution.