We explore the roles of topology and time-reversal symmetry in one-dimensional superconducting systems. Specifically, we examine junctions involving time-reversal-invariant topological superconductors, which are characterised by the emergence of zero-energy Majorana- Kramers pairs at their boundaries. For Josephson junctions composed of these superconductors, we obtain, through a scattering matrix technique valid in a regime where the junction length is much shorter than the superconducting coherence length, exact analytical and numerical results for the Josephson current in terms of a small number of independently measurable junction parameters. The current is found to have a number of prominent and robust features which indicate the underlying symmetries and the nontrivial topology inherent in these systems. The most remarkable of these features occurs in the form of switches in the Josephson current, where the sign of the current reverses as a consequence of crossings between energy levels in the subgap spectrum. By utilising a quantum master equation approach, we establish general conditions under which these switches manifest in relation to a phenomenological relaxation rate and a voltage applied across the junction. Our findings enable quantitative predictions for such junctions, potentially assisting in experimental directions regarding the detection of Majorana- Kramers pairs in mesoscopic Josephson systems.

A bubble chamber experiment is described using data from the C.E.R.N. 2m bubble chamber filled with deuterium and exposed to a 4 GeV/c \(π^+\) beam. Measurements are presented of the U.5. \(π^+\) beam momentum, and the level of contamination in the beam is estimated. A brief review is given of the computer programs used in the processing of 2m bubble chamber film for physics analysis. The channel \(π^+d \rightarrow p_s p π^+ π^- ( \sigma = 2.10^±0.17m b) \) (1) is investigated and cross sections are obtained for the quasi-two-body reactions \(π^+d \rightarrow p_s p \rho^0 ( \sigma = 1.21^±0.16m b) \) (2) and \(π^+d \rightarrow p_a p f^0 ( \sigma = 0.53^±0.06m b) \) (3) An Estabrooks and Martin amplitude analysis is made of reaction (2) using 5279 events from the mass interval \(0.68<M_{ππ} < 0.88 GeV/c^2 \) Results are presented on the spin structure and production mechanism of the \(\rho^0\) meson. A comparison is made of the results of this analysis with those of a higher energy \(π^-p\) experiment and the predictions of an π exchange absorption model. The isospin zero S wave ππ scattering phase shifts are obtained for ππ effective mass less than 1 4 GeV/c². Evidence is presented favouring a set of phase shifts rising slowly through the rho region to be 90° at about 900 MeV/c² in ππ effective mass. An investigation is also made of the branching ratios of the \(f^0\) meson into final states other than \(π^+π^-\). These include \(π^+d \rightarrow p_s p K^+ K^-\) (4) \(π^+d \rightarrow p_s p 2π^+ 2π^-\) (5) \(π^+d \rightarrow p_s p 2π^+ 2π^- π^0\) (6) \(π^+d \rightarrow p_s p π^+ π^- M M\) (7) \(π^+d \rightarrow p_s p 2π^+ 2π^- M M\) (8) where M M indicates missing particles. Evidence is presented for f° decay into channels (4) and (5) and the decay rates are measured.

The thesis focusses on the developments and measurements of the Yb+ optical clock at NPL. During my period there, new ion traps, trap control electronics and optical cavities have been developed. Numerous measurement campaigns have been conducted, where we measured the absolute frequency of both optical clock transitions in Yb+ relative to caesium, for the first time ever directly measured the frequency ratio of these transitions, and performed numerous international comparisons against other optical clocks. The total systematic uncertainty of the clock is now expected to be at the mid-low 10-18 level, with published uncertainty budgets at the mid 10-17 level, making it a strong candidate for a future redefinition of the second. The exotic electron structure of the excited levels in Yb+ make it a promising system for tests of fundamental physics. The frequencies of the transitions used in the Yb+ clock are highly sensitive to changes in the fine structure constant, α, which is predicted to vary by many physical theories beyond the standard model. By combing our absolute frequency measurements with a history of atomic clock measurements, we can place new best limits on the present day time variation of α, and the proton-electron mass ratio, µ.

This thesis describes both experimental and theoretical work on the electronic transport properties of 30 nm InSb/AlInSb quantum well 2DEG heterostructures. Advances in the epitaxial growth of large lattice constant III-V materials using mismatched substrates like GaAs or Si has generated renewed interest in developing high mobility devices. Similarly, narrow gap semiconductors are promising candidates for the advancement of spintronic devices taking advantage of their extreme material parameters, such as the small effective mass and large effective Landé g-factor. An investigation of the low temperature Hall effect and Shubnikov-de Haas oscillations of asymmetrically doped InSb quantum well heterostructures has been made to determine the scattering mechanisms present for carriers in the 2D system. Modelling these oscillations by calculation of the density of states at the Fermi energy as a function of magnetic field was performed to analyse the effects of parameter variation on the observed oscillation. Application of a dielectric layer and gate electrode to the material surface has allowed for a carrier density dependent investigation of the transport properties to be performed. These investigations have provided a detailed understanding of the transport limiting scattering mechanisms over a range of carrier densities and temperatures. A novel study of the current-voltage characteristics of high resistance contacts has been performed to investigate the energetic distribution of electron states in the quantum well under the application of large magnetic fields. Clear Landau level quantisation of the 2D density of states for the first subband of the quantum well has been observed. Analysis of the high field asymmetry of the fundamental Landau level has revealed the presence of significant spin dependent broadening within the heterostructure, which has previously been suggested to exist from an asymmetry of the Fourier transform of Shubnikov-de Haas oscillation.

The resonant-state expansion (RSE) is generalised to open optical systems with an arbitrary dispersion of the dielectric constant. In the non-dispersive case we use frequency independent refractive index, moving onto to cases which display dispersion. The RSE converts the Maxwell wave equation into a linear matrix eigenvalue problem in the basis of unperturbed resonant states, in this way numerically exactly finding all relevant eigenmodes of the optical system. The present generalisation is verified by applying it to the analytically solvable system of a spherical metallic nano-particle in vacuum, with the dispersion of the dielectric constant described by the Drude model and extended with the addition of Lorentz poles. Approximating the frequency dispersion of the permittivity of materials with simple analytical functions is of fundamental importance for understanding and modeling the optical response of materials and resulting structures. In the generalised Drude-Lorentz model, the permittivity is described in the complex frequency plane by a number of simple poles having complex weights, which is a physically relevant and mathematically simple approach: By construction, it respects causality and represents physical resonances of the material, and can be implemented easily in numerical simulations. We report here an efficient method of optimising the fit of measured data with the Drude-Lorentz model having an arbitrary number of poles. We show examples of such optimisations for metals and semiconductors, for different frequency ranges. We use this to produce accurate parameters for us to realistically simulate large perturbations starting from dielectric materials such as sand, to dispersive materials such as gold and gallium arsenide. We also analyse the evolution of surface plasmons in gold and use the RSE to perturb gallium arsenide into the gain threshold.

This thesis presents measurements of spin asymmetries in single pion electroproduction from the EG1-DVCS experiment carried out at the Thomas Jefferson National Accelerator Facility in 2009 with use of the CEBAF Large Acceptance Spectrometer. The experiment made use of a 6 GeV longitudinally polarised electron beam and (dynamically) longitudinally polarised targets of 14NH3 and 14ND3 (giving access to protons and deuterons), providing the means to measure three spin asymmetries: beam-, target-, and double-spin. Deeply Virtual Meson Production for the π0, π+ and π- channels were studied for the kinematic range of Q^2 > 1 GeV^2 and W > 2 GeV. The collection of measurements includes the analysis of numerous reconstruction topologies, as well as making use of different target materials. These are the world's first charged pion spin asymmetry measurements in this kinematic regime. The sPlot maximum likelihood fit-based background subtraction technique was implemented in the data analysis, showing strong agreement with a traditional and commonly used cuts-based approach. This novel technique was thoroughly tested to develop implementation and execution. The results obtained will provide a reference point for future analyses at the upgraded experimental facility and motivate the use of the sPlot technique. These measurements will provide insight into the structure of nucleons through their interpretation in relation to Generalised Parton Distributions which describe substructure correlations between longitudinal momentum and transverse position of partons. In particular, here the spin asymmetries dependence on t, the squared four-momentum transfer to the target nucleon, carries information on the spatial parton distributions in the transverse plane.

It took several decades of intense research and development and the effort of thousands of people to reach the detectors sensitivity that allowed the gravitational waves detectors Advanced LIGO and later Advanced Virgo to make the first detection of gravitational waves on September 14th 2015 (and many other after that). This event marks the birth of gravitational wave astronomy and opens a new window on the universe, giving us the ability to gather information otherwise impossible to obtain. However it is still important to further increase the sensitivity of the interferometers in order to extract more accurately the parameters of the observed gravitational wave sources, as well as to discover new classes of gravitational wave emitters. So research efforts are pursued on all fronts, trying to reduce any relevant sources of noise. One of the proposed methods for the reduction of the quantum noise is based on the concept of quantum non-demolition measurements and speed meters. In this context, a proof-of-concept experiment is underway at the University of Glasgow. The aim of the experiment is to prove that in a Sagnac interferometer, which is per se a speed meter, quantum radiation pressure noise is lower than in an equivalent Michelson at audio-band frequencies. The interferometer designed for this experiment is composed by two triangular cavities with 1 g input test masses and 100 g end test masses and a finesse of ~8000. In this way the sensitivity at low frequencies will be dominated by quantum radiation pressure noise. However these features make the interferometer very sensitive to loss and high quality surface mirrors are then indispensable. The analysis of how much the mirrors surface imperfections will affect the quantum noise in speed meters is indeed the main topic of this thesis. The work carried out can be divided in two parts. The first part consists in the derivation of the arm cavity mirrors surface requirements for the Glasgow Sagnac speed meter. Because of the high dependence of its sensitivity from optical loss, the mirror surface requirements must be very stringent and an in-depth analysis to derive them is presented here. This analysis was done performing simulations that give an estimate of the roundtrip loss generated by each kind of mirror surface imperfection. In particular most of the analyses were done using OSCAR (acronym of Optical Simulation Containing Ansys Results), a Matlab package that can simulate the behaviour of a cavity with arbitrary mirrors surface profiles. The second part of the thesis is a theoretical analysis of the backscattering effect inside a cavity and how much it affects the quantum noise. The backscattering is a mechanism that arises when the intra-cavity beam has non-zero angle of incidence on the arm cavity mirror. Due to microroughness, in fact, the beam can be scattered back in the same direction as the incident beam. It will then couple with the counter-propagating beam and this coupling causes an increment of the quantum noise. The results are applied to the case of the Glasgow Sagnac speed meter and to future large scale interferometers. It is worth noting that the analysis of this newly discovered noise coupling caused by backscattering in speed meters featuring triangular cavities can also be applied to the class of speed meters configurations using linear cavities and two different polarisations, where the coupling of the modes is caused by birefringence.

The research carried out was on the development and study of position sensitive proportional counters and was initiated by Dr. R.W.P, Drever. The first chapter of this thesis is a discussion of the type of experimental problems which require the spatial distribution of ionizing radiation to be investigated and of the different methods of obtaining position information. The possible advantages of a proportional counter system for the localisation of charged particles and love energy x-rays are pointed out. In the following chapter, the main factors which limit the position resolution of any electrical detector are outlined, with particular emphasis on the effect of the thermal diffusion of the charge carriers in semiconductor counters, proportional counters and spark chambers. The material for these two chapters was taken mainly from the literature, although the application of diffusion theory to the calculation of the position resolution in the different detectors was the work of the author. Chapter III includes a general description of the method of charge division on a resistive electrode for obtaining position information from a counter; and the limitations to position linearity and resolution which result from the use of this method (as reported in the literature) are discussed. The electronic system required for a position sensitive proportional counter is described and the design and development by the author of a high precision ratio circuit for this work is outlined. The next chapter is an account of the experimental measurements of resolution and linearity performed by the author on proportional counters which were sensitive to position in one dimension. The position resolutions for single electrons, alpha particles and x-rays were measured, and the experimental resolution for single electrons is compared with the limitations from gas diffusion theory in Chapter V. The data for this comparison was partly drain from the literature; but one of the methods used for calculating the electron diffusion in a gas mixture was devised by the author. The interpretation of the performance of these detectors, in Chapter V, is also that of the writer. Chapter VI deals with the building and operation of a two dimensional position sensitive proportional counter which uses a new method of obtaining the counter signal - from electrodes placed between the anode and the cathode. This method was proposed by Dr. Drever. The counter frame used for this work had been designed initially by him, but a number of important modifications to it were made by the author. The development of the counter and the investigation of its performance were the entire responsibility of the author. The appendix to this thesis is an account of an attempt to observe proportional counter or Oeiger counter operation in a cylindrical detector filled with liquid hexane. This work was initiated and carried out by the writer.

The recent discovery of the Higgs boson by the ATLAS and CMS exper- iments and the subsequent measurements of it properties are the latest vindications of the Standard Model of particle physics. The SM has a number of well known flaws, and the continuing dearth of Beyond the Standard Model signatures from experiment has led to investigations into whether the SM is valid up to very high scales. The motivation for much of this work comes from the quartic Higgs coupling λ and its β function, which run to an extremely small values at high scales. These may be hints of new UV dynamics, in particular the Multiple Point Principle which posits the existence of a second degenerate minimum in the effective potential at the Planck scale, and Asymptotic Safety, where the dimensionless couplings of the potential run towards an interacting UV fixed point. In this work we will investi- gate the possibility for similar high scale boundary conditions in extensions of the Standard Model. Specifically, we look at the Real Singlet model, the Complex Sin- glet model, the Type-II Two Higgs Doublet Model, and the Inert Doublet Model. We will apply the relevant theoretical constraints to the parameter space of theses models, as well as experimental constraints such as those from ATLAS, CMS, LEP, the Tevatron, WMAP, Planck and LUX. Points that pass these constraints will also be investigated for their validity under a number of high scale boundary conditions on its scalar sector, and the valid parameter space will be checked for signatures in the mass spectrum that can be probed by current and future collider experiments.

The T2K long-baseline neutrino experiment in Japan is designed to study neutrino oscillations, to determine the mixing angles and mass-squared difference of the neutrino mass eigenstates and, potentially, to discover CP violation in neutrinos by comparing neutrino to antineutrino oscillations. In the near detector complex 280 m downstream of the produc- tion target at the Japanese Particle Accelerator Research Centre (J-PARC), the WAGASCI experiment will measure the ratio of cross sections from neutrinos interacting with a water and scintillator targets, in order to constrain neutrino cross sections essential for the T2K neutrino oscillation measurements. A prototype Magnetised Iron Neutrino Detector, called Baby MIND, has been constructed at CERN and will act as a magnetic spectrometer behind the main WAGASCI target. The Baby MIND spectrometer was installed between February and March 2018 in the near detector complex, behind WAGASCI and is able to measure the charge and momentum of the outgoing muon from neutrino charged current interactions inside the WAGASCI target, to be able to perform full neutrino event reconstruction. Baby MIND collected data in the reverse horn focussed antineutrino beam between April and May 2018. In this thesis, the Baby MIND spectrometer is described in detail along with the performance from initial beam tests performed with the Proton Synchrotron (PS) charged particle beam at the T9 test beam facility at CERN. The test beam was used to perform measurements of track reconstruction efficiency and charge reconstruction efficiency, using dedicated reconstruction programmes, SaRoMaN and SAURON. The software environment used to perform event reconstruction in the complex detector geometry of Baby MIND is described in this thesis. Furthermore, a machine learning multi-variate analysis was used to perform particle identification between muons and hadrons, allowing for a pure selection of muons in the test beam. NuSTORM is a novel type of neutrino beam from the decay of muons in a storage ring. This type of facility produces well defined beams of $\nu_\mu$ and $\bar{\nu_e}$ neutrinos. A study is performed in the thesis to determine the expected sensitivity of mea- suring neutrino interactions in a fully active scintillator neutrino target, with a magnetised iron detector downstream. This analysis also benefited from an identification of the different event types by using a machine learning multi-variate approach. Finally, results are presented on charged current quasi-elastic neutrino and antineutrino interactions in iron reconstructed with the Baby MIND detector during the 2018 neutrino data taking at J-PARC.