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.

General relativity is the successful classical theory describing gravitational interactions from cosmological scales down to the sub-millimetre scale. It has remained an open challenge to combine the principles of general relativity with those of the quantum world. A promising avenue has been put forward by Steven Weinberg, known as the asymptotic safety conjecture for gravity. It stipulates that a quantum field theory of gravity may very well exist as a fundamental and predictive theory up to highest energies. The central ingredient of this scenario is the existence of an interacting ultraviolet fixed point under the renormalisation group running of gravitational couplings. In this thesis, we study several aspects of asymptotic safety for gravity. Firstly, we offer a detailed qualitative and quantitative analysis of modern renormalisation group equations for Einstein-Hilbert gravity by contrasting different implementations of a Wilsonian momentum cutoff in combination with either heat kernel techniques or spectral sums. Secondly, we analyse in some depth the scale-dependence of gravitational couplings in the low-energy regime of Einstein-Hilbert gravity, where indications for the existence of an interacting infrared fixed point are found. Finally, we extend our analysis of renormalisation group trajectories to f(R)-type theories of gravity, and investigate how an interacting UV fixed point is connected with the classical low-energy regime. Implications of our findings are discussed.

We study quantum (T = 0) phases of strongly-correlated matter, and their possible implementation in a quantum simulator. We focus on the non-perturbative regimes of 1D spin-boson models. As a reference physical system we consider trapped-ion chains. We realize complex many-body states, such as a ground state exhibiting magnetic frustration, a lattice gauge theory, and a topological insulator. The exquisite control over these phases offered by a quantum simulator opens up exciting possibilities for exploring the exotic phenomena emerging in these systems, such as enhanced fluctuations and correlations. We address the non-perturbative regimes of the phase diagrams by means of mean-field theories and the numerical algorithm DMRG. We have established the universality class of the continuous transition in the spin-boson chain, the existence of a first order phase transition when the system is endowed with a gauge symmetry, and the possibility of probing topological states of matter in these systems. Our results show that some of the most exotic phases of quantum matter can be readily realized in trapped-ion quantum simulators. This offers the possibility of exploring these physical models beyond their original realm of applicability, which may provide us with new insights on both theoretical and applied fields of physics, ranging from high-energy processes to low-energy cooperative phenomena.

The many-electron Schrödinger equation for atoms and molecules still remains analytically insoluble after over 90 years of investigation. This has not deterred scientists from developing a large variety of elegant techniques and approximations to workaround this issue and make many-particle quantum calculations computationally tractable. This thesis presents an all-particle treatment of three-particle systems which represent the simplest, most complex, many-particle systems including electron correlation and nuclear motion effects; meaning they provide a close-up view of fundamental particle interaction. Fully-Correlated (FC) energies and wavefunctions are calculated to high accuracy (mJ mol−1 or better for energies); and the central theme of this work is to use the wavefunctions to study fundamental quantum chemical physics. Nuclear motion has not received the same attention as electronic structure theory and this complicated coupling of electron and nuclear motions is studied in this work with the use of intracule and centre of mass particle densities where it is found nuclear motion exhibits strong correlation. A highly accurate Hartree-Fock implementation is presented which uses a Laguerre polynomial basis set. This method is used to accurately calculate electron correlation energies using the Löwdin definition and Coulomb holes by comparing with our FC data. Additionally the critical nuclear charge to bind two electrons within the HF methodology is calculated. A modification to Pekeris' series solution method is implemented to accurately model excited states of three-particle systems, and adapted to include the effects of nuclear motion along with three Non-Linear variational Parameters (NLPs) to aid convergence. This implementation is shown to produce high accuracy results for singlet and triplet atomic excited S states and the critical nuclear charge to bind two electrons in both spin states is investigated. Geometrical properties of three-particle systems are studied using a variety of particle densities and by determining the bound state stability at the lowest continuum threshold as a function of mass. This enables us to better ascertain what is meant when we define a system as an atom or a molecule.

The Super-K experiment determined that neutrinos are massive particles by observing the oscillation of atmospheric neutrinos. The SNO experiment confirmed this measurement by observing neutrinos from the Sun. The SNO+ experiment is intended to study the nature of neutrino masses by replacing the heavy water used in SNO with scintillator. The main goal of the experiment is to search for neutrinoless double-beta decay within 130Te. The SNO+ detector is much more sensitive to radioactive contamination than the SNO experiment. For this reason an external LED calibration system has been developed so the detector can be calibrated without risking contamination of the scintillator volume. This thesis describes the commissioning of this calibration system and its performance during the water phase of SNO+. The scintillator volume is separated from the surrounding detector via an acrylic vessel. As scintillator is less dense than water the position of the vessel is expected to shift throughout the lifetime of SNO+. A method to determine the position of the vessel using the external LED system is detailed as well as its performance. A measurement of the scattering length of the water surrounding the acrylic vessel using the same LED system is also presented. Calibration of the detector will also be performed using sources deployed within the vessel, and a study on the angular distribution of light from these sources and the effect of hardware upgrades is also presented. During the lifetime of the SNO+ experiment, the detector will be sensitive to neutrinos emitted from a supernovae within the Milky Way. A software framework was developed to accurately simulate the main interaction channels for supernova neutrinos within SNO+. The software was used to determine the burst trigger effciency during the water phase as well as a procedure to follow in the case of the burst. One outstanding problem in the field of neutrino physics is the neutrino mass hierarchy; whether there are two heavy and one light or two light and one heavy neutrino mass eigenstates. Neutrinos from a supernova burst may be able to solve this problem. A simple study is performed to determine the sensitivity of various detectors. The same analysis is performed using the aforementioned software to explore any systematic effects which may alter the sensitivity.

Trapped ions within Paul traps have shown to be a promising architecture in the realisation of a quantum information processor together with the ability of providing quantum simulations. Linear Paul traps have demonstrated long coherence times with ions being well isolated from the environment, single and multi-qubit gates and the high fidelity detection of states. The scalability to large number of qubits, incorporating all the previous achievements requires an array of linear ion traps. Microfabrication techniques allow for fabrication and micron level accuracy of the trap electrode dimensions through photolithography techniques. The first part of this thesis presents the experiential setup and trapping of Yb+ ions needed to test large ion trap arrays. This include vacuum systems that can host advanced symmetric and asymmetric ion traps with up to 90 static voltage control electrodes. Demonstration of a single trapped Yb+ ion within a two-layer macroscopic ion trap is presented. with an ion-electrode distance of 310(10) μm. The anomalous heating rate and spectral noise density of the trap was measured, a main form of decoherence within ion traps. The second half of this thesis presents the design and fabrication of multi-layer asymmetric ion traps. This allows for isolated electrodes that cannot be accessed via surface pathways, allowing for higher density of electrodes as well as creating novel trap designs that allow for the potential of quantum simulations to be demonstrated. These include two-dimensional lattices and ring trap designs in which the isolated electrodes provide more control in the ion position. For the microfabrication of these traps I present a novel high-aspect ratio electroplated electrode design that provides shielding of the dielectric layer. This provides a means to mitigate stray electric field due to charge build up on the dielectric surfaces. Electrical testing of the trap structures was performed to test bulk breakdown and surface flashover of the ion trap architectures. Results showed sufficient isolation between electrodes for both radio frequency and static breakdown. Surface flashover voltage measurements over the dielectric layer showed an improvement of more than double over previous results using a new fabrication technique. This will allow for more powerful ion trap chips needed for the next generation of microfabricated ion trap arrays for scalable quantum technologies.