A search for long transient gravitational waves associated with neutron stars is presented. The estimated length of these sources is from hours to weeks. Two types of astrophysical sources are considered: pulsar timing glitches associated with r-modes oscillations in the interior of isolated neutron stars, and Type I X-Ray bursts in neutron stars from binary systems. These signals follow the model of an e-folding sinusoid signal with a duration dependant on dissipation processes in the interior of the neutron stars and the gravitational radiation reaction. Estimations of the timescales of gravitational wave signals emitted by stable stars are presented. From this study, it is concluded that detecting signals from faster spinning neutron stars is more feasible than from slower neutron stars. The study of this type of transient gravitational wave signals is explored for the first time using an adaptation of the F-statistic gravitational wave search method used regularly in continuous gravitational wave searches. This adaptation, proposed by Prix et al, is a search methodology in which the duration of a signal plays a significant role in its detection. This code is part of the LAL/LAL-apps data analysis algorithm libraries of the LIGO and VIRGO scientific collaborations (LVC). The use of this method in the gravitational wave search presented in this thesis was implemented in two different environments: gaussian noise data and data in gravitational wave detector-like noise. For the latter, injections of long transient signals with durations ∼ 10,000 s on the LVC Engineering Run 3 were done. A comparison between the results obtained in these two studies is presented. It shows that, by having a good characterisation of unwanted noise lines, it is possible to distinguish the frequency of the injected signal within a small search band of only a few frequency bins. On the other hand, the recovery of the duration of the signal would require a broad search band over time. This estimation is set to be approximately ±τ, where τ is the damping time of the injected signal, in order to construct a complete τ distribution. For example, for a signal that last ∼ 3.5 days, an total τ interval of ∼ 6.5 − 7 days is required.

Formal methods is an area in theoretical computer science that provides the theories and tools for describing and verifying the correctness of computing systems. Usually, such systems comprise of concurrent and communicating components. The success of this field led to the development of quantum formal methods by transferring the ideas of formal methods to quantum systems. In particular, formal methods provides a systematic methodology for verification of systems. Quantum process calculus is a specialised field in quantum formal methods that helps to describe and analyse the behaviour of systems that combine quantum and classical elements. We focus on the theory and applications of quantum process calculus in particular to use Communicating Quantum Processes (CQP), a quantum process calculus, to model and analyse quantum information processing (QIP) systems. Previous work on CQP defined labelled transition relations for CQP in order to describe external interactions and also established the theory of behavioural equivalence in CQP based on probabilistic branching bisimilarity. This theory formalizes the idea of observational indistinguishability in order to prove or verify the correctness of a system, and an important property of the equivalence is the congruence property. We use the theory to analyse two versions of a quantum error correcting code system. We use the equational theory of CQP from the previous work and define an additional three new axioms in order to analyse quantum protocols comprising quantum secret-sharing, quantum error correction, remote-CNOT and superdense coding. We have expanded the framework of modelling in CQP from providing an abstract view of the quantum system to describe a realistic QIP system such as linear optical quantum computing (LOQC) and its associated experimental processes. By extending the theory of behavioural equivalence of CQP, we have formally verified two models of an LOQC CNOT gate using CQP. The two models use different measurement semantics in order to work at different levels of abstraction. This flexibility of the process calculus approach allows descriptions from detailed hardware implementations up to more abstract specifications. The orbital angular momentum (OAM) property of light allows us to perform experiments in studying higher dimensional quantum systems and their applications to quantum technologies. In relation to this work, we have extended CQP to model higher dimensional quantum protocols.

Computational imaging with single-pixel detectors utilises spatial correlation of light to obtain images. A series of structured illumination is generated using a spatial light modulator to encode the spatial information of an object. The encoded object images are recorded as total intensities with no spatial information by a single-pixel detector. These intensities are then sent to correlate with their corresponding illumination structures to derive an image. This correlation imaging method was first recognised as a quantum imaging technique called ghost imaging (GI) in 1995. Quantum GI uses the spatial correlation of entangled photon pairs to form images and was later demonstrated also by using classical correlated light beams. In 2008, an adaptive classical GI system called computational GI which employed a spatial light modulator and a single-pixel detector was proposed. Since its proposal, this computational imaging technique received intensive interest for this potential application. The aim of the work in this thesis was to improve this new imaging technique into a more applicable stage. Our contribution mainly includes three aspects. First an advanced reconstruction algorithm called normalised ghost imaging was developed to improve the correlation efficiency. By normalising the object intensity with a reference beam, the reconstruction single-to-noise ratio can be increased, especially for a more transmissive object. In the second work, a computational imaging scheme adapted from computational GI was designed by using a digital light projector for structured illumination. Compared to a conventional computational GI system, the adaptive system improved the reconstruction efficiency significantly. And for the first time, correlation imaging using structured illumination and single-pixel detection was able to image a 3 dimensional reflective object with reasonable details. By using several single-pixel detectors, the system was able to retrieve the 3 dimensional profile of the object. In the last work, effort was devoted to increase the reconstruction speed of the single-pixel imaging technique, and a fast computational imaging system was built up to generate real-time single-pixel videos.

The Real Compton Scattering experiment was performed in all A at the Thomas Jefferson National Accelerator Facility. It was designed to measure, for Compton scattering and π 0 -photoproduction, the differential cross section over a range of kinematic points and the polarisation transfer to the proton at a single kinematic point. The full range of the experiment in Mandelstam variables t and s was 1.64−6.46 GeV 2 and 4.82−10.92 GeV 2 respectively with beam energies of 2−6 GeV. The motivation for the experiment is to test the cross section and polarisation trans- fer predictions of perturbative QCD versus that of predictions from Generalised Parton Distribution models. This thesis will give an overview of the pertinent theory, experimental setup in Hall A and the extracting of the π 0 -photoproduction cross section.

The top quark is the heaviest particle in the Standard Model, with a strong coupling to the Higgs boson. It is often seen as a window to new physics, therefore understanding its production is a key ingredient for testing the Standard Model or physics Beyond the Standard Model. In this document, the production cross section of top-antitop pairs in its semileptonic decay channel is measured as a function of the jet multiplicity in the ATLAS experiment, using proton-proton collisions at the center-of-mass energy of sqrt(s) = 7 TeV. The top-antitop production with extra jets is the main background for many analyses, including the top-antitop-Higgs production studies. The analysis performed is extended in a search for Beyond the Standard Model physics which predicts a resonance decaying in a top-antitop pair, using ATLAS data at center-of-mass energy of sqrt(s) = 7 TeV. The latter analysis is repeated for ATLAS data collected with sqrt(s) = 8 TeV. Performance studies of b-tagging algorithms in the ATLAS Trigger System are also presented.

With the development of pixelated liquid crystal displays, a new paradigm has emerged in the field of optics. Essentially, these displays enable interfacing a computer program with light, and therefore allow a wide range of light beams to be created. In this thesis, I shall be using liquid crystal displays to create phase diffraction patterns and, in this case, the displays are more commonly referred to as Spatial Light Modulators (SLMs). One area where SLMs have shown particular promise is that of optical microscopy. Here, they have been used in two different applications, namely holographic optical tweezers and SLM microscopy; this thesis concerns both. The aim of the thesis is to explore and develop new techniques combining SLMs with microscopy. The first part of this thesis goes into results of the experiments I have carried out in holographic optical tweezers. Hydrodynamic interactions play an important role in many physical and biological processes. I present experimental evidence for the partial synchronisation of the stochastic oscillations of two spheres in a bistable optical trap. This experiment showed that, even in the absence of an external driving force, a degree of synchronisation still exists due to the Brownian motion alone. I then describe a new procedure to protect the optical trap from contamination in sensitive samples. Microrheology using optical tweezers requires lengthy position measurements in order to obtain the linear viscoelastic properties of fluids and this measurement is often compromised by freely diffusing material entering the trap. I then apply rotational Doppler velocimetry to a particle spinning in an optical tweezers. This is the first time that structured illumination has been used to determine rotation rate in the micro regime. The second part describes the development of an SLM microscope and a series of experiments I carried out with it. The set up of the microscope is described and images are characterised in terms of the point spread function. I also demonstrate the multimodal capabilities by diffracting three different images, each with a unique spatial frequency filter, onto a single camera chip. Next, I report the development of some new frequency filters, namely holographic stereo microscopy and three variations, including stereo with defocus which mimics human binocular vision where we have two eyes (views) of the world, each having its own lens. I used 3D particle tracking to investigate sedimentation in a confined microscope sample. This experiment brought together SLM microscopy and optical tweezers to create a new technique for particle sizing, or study surface effects. This thesis describes several new applications of SLMs in microscopy, with the common theme being that the SLM is placed in the Fourier plane of the sample. Both holographic optical tweezers and SLM microscopy have been expanded by the techniques I have developed. In future, this work will serve as foundation for the combination for 3D particle tracking and visualisation with SLM microscopy, whilst microrheology will benefit from the new approaches.

The existence of Gravitational waves is a prediction that arose from Einstein's theory of general relativity. So far their direct detection has eluded scientists with Einstein himself believing they would never be detected. However, recent developments in advanced interferometric detectors should allow the first detections to be made when they are commissioned later this decade. This will open up an entire new field of astronomy giving deeper understanding to the physics of and proving Einstein's general theory of relativity. Astronomers always want bigger telescopes whether it is to see further or to see more detail and this will no doubt occur with gravitational wave telescopes. Hence, further improvements in sensitivity will be required. This thesis examines techniques for improving sensitivity beyond the standard quantum limit, a future limit to sensitivity, using optical rigidity. By coupling two suspended cavity mirrors together using only the light circulating between them the response of the system changes such that a linear restoring force is created on both cavity optics, the "optical spring". The first experiment carried out in the scope of this thesis shows how an intentionally applied signal that changes the position of the input mirror in a rigidly coupled cavity is transferred via the optical spring to a position change of the output cavity mirror. A small independent interferometer, a so-called local readout, is used to monitor the displacement of the output cavity mirror allowing the position of the input mirror to be inferred. This experiment verifies that it is possible to gather information on the position of the input mirror via the local readout interferometer the photons of which have never interacted with the input mirror. The local readout device was able to measure a coupled motion between the cavity mirrors, via the optical spring, of 10⁻¹³m at 922 Hz. Hence this experiment can be considered as the first demonstration of an optical bar configuration which has been previously shown to be a type of quantum non-demolition measurement. In the second experiment an optical spring, present in a 10m cavity used as a frequency reference, provides a peak in the optical gain of this cavity. The peak in gain, due to the resonance of the optical spring, is then shown to enhance the frequency stability of the 10m cavity around the optical spring frequency. An increase in sensitivity of 3 dB across a 50 Hz window centred around 200 Hz was measured showing that this is a good example of how the optical spring can also be used to improve high-precision classical measurements. Overall this thesis provides examples of how optical springs can be used as a building block for improvements of high precision interferometry and quantum measurement. These technologies are likely to play a key role in future gravitational wave detectors such as the Einstein Telescope.

As electronics become more and more miniaturised, there is much interest in increasing knowledge about the electronic and transport properties of nano-systems. In particular, there has been some focus on understanding the physics of nanowires with prescribed properties. Two different groups of systems have been considered that of 1D organic molecular nanowires and 2D interconnects based on graphene. In order to develop a deeper insight of the factors that determine the electronic structure and consequently the electrical transport properties, it is desirable to carry out computer simulation studies of these systems. The work reported in this thesis has focused on studying the porphyrin and DNA molecules as well as investigating the consequences of engineered 2D graphene interconnect. The latter class of systems has included graphene nanoribbons (GNRs), graphene sheets with grain boundaries (GGBs) and graphene nanomeshes (GNMs). The methodology was to use self-consistent extended Hückel theory (SC-EHT) and density functional theory (DFT) in combination with non-equilibrium Green functions (NEGFs) formalism to investigate the electronic and transport properties of these systems. The SC-EHT calculations were performed using an in-house developed C++ code named EHTransport. While the SIESTA package was employed for the DFT. It was found that the SC-EHT approach produced comparable results with that obtained by DFT. This supports the idea that the semi-empirical methods can be as valid as ab-initio approaches. The findings demonstrated that porphyrin, DNA, and graphene based systems are very promising candidates to incorporate in future electronics.

This thesis presents work that I have done with Egor Muljarov and Wolfgang Langbein in order to extend an existing perturbation theory for open systems describable by a scalar equation to 3D systems which cannot be reduced to effectively lower dimensions. This perturbation theory is called the resonant-state expansion (RSE). The RSE is derived from properties of the dyadic tensor Green’s function (GF) of the unperturbed system written in terms of resonant states (RSs). Hence to extend the RSE it was necessary for us to derive this spectral form of the GF in terms of normalised RSs for arbitrary 3D systems. To process the numerical output of the RSE, we develop and evaluated algorithms for error estimation and their reduction by extrapolation. In the case of planar systems the RSE can be compared with other methods such as the scattering matrix or transfer matrix methods. It is also possible to solve the boundary conditions analytically to provide transcendental equations that can be solved by the Newton-Raphson method. We study these systems for that reason since we can validate the numerical calculations of the RSE by showing the convergence of perturbed solutions to the exact result found from these other methods. We study the planar systems both zero and non-zero in-plane wavevector. As an intermediate step to a fully 3D perturbation theory for open systems we make an implementation of the RSE in 2D. We use as a basis the analytically known RSs of the infinitely extended homogeneous dielectric cylinder. We find that the unperturbed GF contains a cut in the complex frequency plane, which must be included in the RSE basis for the accuracy of the perturbation theory. Zero frequency longitudinal modes are found to be formal solutions of Maxwell’s wave equation which also must be included in the basis for the accuracy of the method. Zero frequency modes occur for systems of all dimensionality when considering the TM modes, modes with electric field component normal to the interfaces. In the penultimate chapter of this thesis we apply the RSE to fully 3D open systems. We use as a basis the analytically known RSs of the homogeneous dielectric sphere. This advance was non-trivial due to a general mixing of transversal and longitudinal electro-magnetic modes. We compare the performance of the RSE with available commercial electromagnetic solvers. In the case of 3D perturbations, we find that the RSE provides a higher accuracy than the finite element method (FEM) and finite difference in time domain (FDTD) for a given computational effort, demonstrating its potential to supersede presently used methods. At the end of the penultimate chapter we introduce a local perturbation method for RSE, which is a unique capability of the RSE compared to FEM or FDTD, and allows to calculate small perturbations of a system with a small computational effort.

This thesis focuses on physical measurements of the sound radiated by stringed musical instruments. The radiation efficiency, defined as the ratio of acoustical power output to mechanical power input, was measured to study the acoustical behaviour of the instruments between 80 Hz and 2000 Hz. The research used spherical-harmonic decomposition to determine the power output from monopole and dipole sources. On classical guitars, monopole power produced by the low-frequency resonance triplet provided the greatest contribution to the power output below 300 Hz. At higher frequencies, where the body modes have more complex shapes, dipole sources dominated the total power output. As the dipole contribution to the power output increases, the radiation efficiency of the instrument decreases. The research demonstrated that the resonance frequencies of the body modes of the instruments do not correspond with either a large or small value of radiation efficiency. Instead it is the mode shape that determines the radiation efficiency. Modes with similar-sized anti-nodal areas, of opposite phase, were found to be less efficient than modes which had unequal-sized anti-nodal areas. Measurements of the in-plane velocity of these modes, made with a 3D scanning laser vibrometer, showed that the less-efficient modes had greater values of in-plane velocity. The largest values of radiation efficiency for classical guitars occurred between 200 Hz and 600 Hz. The upper frequency limit of this range was determined by the resonance frequency of a particular mode. This was confirmed by experiments on a purpose-built guitar in which the cross-grain stiffness could be adjusted. Experiments on classical guitars, steel-string guitars and violins produced characteristically different radiation efficiencies.