This thesis applies techniques of non-perturbative quantum field theory for solving both bosonic and fermionic systems dynamically on a lattice. The methods are first implemented in a bosonic system to examine the quantum decay of a scalar field oscillon in 2+1D. These configurations are a class of very long-lived, quasi-periodic, non-topological soliton. Classically, they last much longer than the natural timescales in the system, but gradually emit energy to eventually decay. Taking the oscillon to be the inhomogeneous, (quantum) mean field of a self-interacting scalar field enables an examination of the changes to the classical evolution in the presence of quantum fluctuations. The evolution is implemented through applying the Hartree approximation to the quantum dynamics. A statistical ensemble of fields replaces the quantum mode functions to calculate the quantum correlators in the dynamics. This offers the possibility for a reduction in the computational resources required to numerically evolve the system. The application of this method in determining the oscillon lifetimes, though, provides only a negligible gain in computational efficiency: likely due to the lack of any space or time averaging in measuring the lifetimes, and the low dimensionality. Evolving a Gaussian parameter-space of initial conditions enables comparing the classical and quantum evolution. The quantum fluctuations significantly reduce the lifetime compared to the classical case. Examining the evolution in the oscillatory frequency demonstrates the decay in the quantum system occurs gradually. This markedly contrasts the classical evolution where the oscillon frequency has been demonstrated to evolve to a critical frequency when the structure abruptly collapses. Despite the distinctly different evolution and lifetime, a similar range of the Gaussian initial conditions in both cases generates oscillons. This indicates the classical effects dominate the early evolution, and the quantum fluctuations most significantly alter the later decay. The methods are next implemented in a fermionic system to examine "tunnelling of the 3rd kind". This phenomenon is examined in the case where a uniform magnetic field propagates through a classical barrier by pair creation of fermions: these cross unimpeded through the barrier and annihilate to (re-)create the magnetic field in the classically shielded region. A statistical ensemble of fields, similarly to the oscillon simulations, is initially constructed for evaluating the fermionic contribution in the gauge field dynamics. This ensemble, importantly and in contrast to the bosonic case, involves two sets of fields to reproduce the anti-commuting nature of the fermion operator. The ensemble method, again, offers the possibility for a reduction in the computational resources required to evolve the system numerically. A test case indicates the method for the tunnelling system, though, requires impracticable computational resources. Using the symmetries in the system to construct an ansatz for the fields provides an alternative method to evolve the dynamics on a lattice. This procedure effectively reduces the system to a 1+1 dimensional problem with the fermion mode functions summed over the three-dimensional momentum space. The significant decrease in the real-time for the evolution (and quite attainable computational resources) on applying the ansatz provides a practical technique to examine the tunnelling. Measuring the magnetic field in the classically shielded region confirms the analytic estimates. These (qualitatively) reproduced the exponential decrease estimated in the classical transmission on varying the interaction strength between the barrier and the magnetic field. The observed tunnelling signal, moreover, matches the perturbative, analytic estimate within the expected correction in the lattice configuration. These bosonic and fermionic quantum, dynamical simulations demonstrate limitations to the benefits in applying the ensemble method. The highly practical and successful tunnelling computations, in contrast, indicate the potential power of a suitable ansatz to significantly reduce the computational times in simulations on a lattice.

This thesis analyzes competing theories of constitutional interpretation. Originalism as traditionally understood maintains that proper constitutional interpretation involves consulting the historical record for what the words meant at the time of ratification. This position is in stark opposition to moral reading, which views certain constitutional provisions as embodying broad philosophical principles that must be interpreted according to the best understanding of our constitutional commitments. Originalism seeks historical truths of constitutional meaning whereas moral reading aims primarily toward ethical adjudication and constitutional perfection. I track the origins of originalism and its development in American legal scholarship while analyzing the interpretive shortcomings and ethical dilemmas the theory poses. I ultimately reject originalisms as traditionally conceived as antithetical to American constitutional ideals, as blind to the teachings of this Nation’s jurisprudential history, and as more theoretically problematic than the moral reading it attempts to combat. I further contend that the newest wave of originalist thinking, which recognizes broad constitutional commitments, is no more than moral reading in disguise. I conclude that moral reading is a more defensible theory of constitutional interpretation and that new originalists ultimately agree.

Thesis (Ed.M.)--Boston University

Magnetic memory technology, especially hard disk drives are the leading technology for storing data. Increasing demand for improved storage density, along with faster processing times and low power consumption, have led to the invention and exploration of more sophisticated technologies based on magnetism. In these state of the art technologies, the primary aim is to manipulate the magnetisation state of the material in order to store information. In the next generation of magnetic memory technologies, the manipulation of the magnetisation state by an external magnetic field has been replaced with electric current or electric field. More recently, the use of strain mediated magnetoelastic coupling to change the magnetisation has attracted a lot of interest for development of energy efficient logical processing and information storage devices. One method to demonstrate this is to use a hybrid piezoelectric/ferromagnetic device. A voltage across the piezoelectric transducer induces a mechanical strain in the ferromagnetic layer and results in the manipulation of the magnetic anisotropy via the inverse magnetostriction effect. In this thesis, hybrid structures of a piezoelectric transducer and a magnetostrictive ferromagnet alloy of Fe 1−x Ga x have been used to investigate the strain manipulation and control of magnetisation. The Fe rich Fe-Ga alloy has demonstrated enhanced values of magnetostriction and has been shown to be very magnetically sensitive to strain both in bulk crystals and in thin film cases. Due to a very high magnetostriction value of (3/2) λ100 = 395 ppm, and no rare earth constituents, the material is a competitive candidate for strain mediated magnetic storage devices. The investigations described in the thesis are on 5 nm bilayer films of Fe 1−x Ga x deposited on GaAs (001) substrates by the magnetron sputter deposition technique. The ferromagnetic layers were separated by either a Cu or Al spacer layer of thickness 5 nm or 10 nm. The grown ferromagnetic layers had different Ga concentration so that they demonstrate different magnetostriction value and the magnetisation reversal process in each layer will be unique and independent. SQUID magnetometry along with ferromagnetic resonance experiments and mathematical modelling of minimising the free magnetic energy, revealed that there is a strong cubic magnetocrystalline anisotropy in the individual layers which was approximately equal for all the samples. The uniaxial anisotropy varied in each of the grown samples due to variation in the interface bonds between the substrate and the metallic stack. By modelling each of the layers to be independent, and solving at the switching field regions, the domain wall depinning energies for each layers have also been estimated. It is revealed that the domain wall depinning energies for the layers grown on the substrate is weaker than the layer grown on the metallic stacks. Ferromagnetic resonance experiments along with mathematical modelling were also used to investigate the dynamic properties of these bilayer films. The role of magnetic anisotropies and spacer type and thickness on the magnetisation precession in terms of the resonance frequency, Gilbert damping and linewidth have been investigated. A narrow linewidth of 3.8 mT and 4.7 mT for the top and bottom layers with a low Gilbert damping value of approximately 0.015 and 0.019 have been obtained which makes these films a competitive candidate for applications of microwave spintronic devices. An investigation of the effects of strain on the magnetisation reversal is described in chapter 4, by employing magnetotransport measurements on processed Hall bar devices mounted on piezoelectric transducers. The measured transport data containing contributions from the anisotropic magnetoresistance and giant magnetoresistance effects arising from distinct magnetisation reversal processes of each layer which were independent for each layer and dependent on the voltage induced strain. This strain-mediated modification of the measured resistances was different for all the samples. The induced strain changed the switching fields of the individual layers and was found to be higher for the 5 nm Al spacer samples than the 5 nm Cu spacer samples. However, the 5 nm Cu sample demonstrated a higher giant magnetoresistance contribution to the measured longitudinal resistance. Finally, the working parameters for a multi-level memory cell operated by voltage-induced strain and based on the layers studied in this thesis have been determined. The conceptualised device is an attractive candidate for high density magnetic information storage. The extension to more than one layer would increase the possible storage density by utilising the third spatial dimension to stack storage elements.

The fast development of quantum technologies requires a new theoretical effort to characterize their performance in practical scenarios. By studying both discrete and continuous variable systems, we will explore several research lines, such as control theory, quantum metrology and non-Markovianity. The thread connecting these different fields will be an approach that attempts to determine the limits and the potentiality of quantum performance in the presence of noise and scarcity of resources. Indeed, the goal of this thesis is to investigate whether quantum features can enhance the performance of particular instances of quantum protocols, and, if this is the case, how this enhancement is affected when some restrictions on the practical implementation of these protocols are in place.

In this thesis we explore aspects of dynamics of open quantum systems related to coherence and quantum correlations - necessary resources for enhanced quantum metrology and quantum computation. We first discuss limits to the precision of parameter estimation when using a quantum system in the presence of noise. To this end we introduce a variational principle for the quantum Fisher information (QFI) bounding the estimation errors of any measurement, which motivates an efficient iterative algorithm for finding optimal system preparations for noisy estimation experiments. Furthermore, we investigate influence of noise correlations on the precision in phase and frequency estimation, by delivering bounds for both spatially and temporarily correlated (non-Markovian) dephasing noise. This allows us to prove the Zeno limit in frequency estimation, conjectured in Phys. Rev. A 84, 012103 (2011) and Phys. Rev. Lett. 109, 233601 (2012). The enhanced estimation precision in quantum metrology can be, however, achieved only using highly entangled states. We propose a scheme of generating such highly correlated states as outputs of Markovian open quantum systems near first-order dynamical phase transitions. We show that the quadratic scaling of the QFI with time is present for experiments within the correlation time of the dynamics and describe a theoretical scheme for quantum enhanced estimation of an optical phase-shift using the photons being emitted from an intermittent quantum system. Finally, we establish the basis for a theory of metastability in Markovian open quantum systems, by extending methods from classical stochastic dynamics. We argue that the partial relaxation into long-lived metastable states - distinct from the asymptotic stationary state - may preserve initial coherences within decoherence-free subspaces or noiseless subsystems, thus allowing for quantum computation during the metastable regime.

Atom chips are an excellent tool for studying ultracold degenerate quantum gases, due to the high degree of controllability afforded by the precise potentials generated from the current-carrying microfabricated wires on the chip surface. The geometries of the trapping potentials are inherently capable of realising extreme aspect ratios, and therefore creating model systems with effectively reduced dimensionality, particularly the theoretically-tractable one-dimensional Bose gas. In addition, the temporal tunability makes it possible to impart non-adiabatic changes on the trapping potentials, allowing experimental investigation of samples which have been brought out of equilibrium - a situation which is not fully theoretically understood. This thesis describes the implementation, development and characterisation of an experimental system for producing the first Bose-Einstein condensates of atomic rubidium 87 gas trapped on the surface of an atom chip in Nottingham. Such an apparatus is very complex and requires careful characterisation in order to run in a stable and reliable way. Details of the experimental setup are thoroughly outlined, including the vacuum system, lasers, electronics, computer control and timing, and the optical imaging system. A newly installed compact two-dimensional magneto-optical trap provides an loading rate of 5e7 atoms per second for loading a three-dimensional mirror-magneto-optical trap with 1.5e8 atoms, at a temperature of 300uK within 10s. The cloud is then sub-Doppler cooled to 50uK, and spin-polarised with 96% purity into the |F=2,mF=+2 > ground state within 5ms, in preparation for loading a purely magnetic trap. A millimeter sized copper Z-shaped conductor located beneath the atom chip surface creates a Ioffe-Pritchard magnetic trap, into which the laser cooled cloud is loaded with 70% efficiency, and can be held with a vacuum-limited lifetime of 40s. Evaporative cooling then pre-cools the sample to below 20uK within 10s, to allow the subsequent loading into potentials created by the atom chip with 100% efficiency. A final evaporation stage then cools the cloud below the phase transition temperature of 800nK, resulting finally in pure BECs with $10^5$ atoms confined using the atom chip. Key measurements of various properties of the trapped condensates are presented, which are important in order to characterise the system fully, and to compare with theoretical expectations. In particular, included are the variation of condensate fraction with temperature, the BEC expansion dynamics, and the condensate lifetime in the trap, for example. Finally, it is demonstrated how BECs can be produced on the atom chip without the use of external macroscopic coils, achieved by using novel, integrated sheet structures located beneath the chip surface - unique to this experimental system - to create the necessary bias fields.

The description of a quantum system follows a fundamentally different paradigm to that of a classical system, leading to unique yet counter-intuitive properties. In this thesis we consider some of these unique properties, here termed simply the quantum. We focus on understanding some important types of the quantum: quantum coherence and quantum correlations, as well as quantum entanglement as an important subclass of quantum correlations. Our objective is to investigate how to quantify the quantum, what it can be used for, and how it can be preserved in the adverse presence of noise. These findings help to clarify the frontier between quantum and classical systems, a crucial endeavour for understanding the applications and advantageous features of the quantum world.

A highly integrated device capable of interfacing light and matter on a chip is presented. 1e7 caesium-133 atoms are captured from a hot vapour into a magneto-optical trap held close to a chip-mounted single-mode fibre. Sub-Doppler optical molasses cools the atoms and transfers them into a tightly focused 18W vertical optical dipole trap which intersects a 30um void that has been laser etched through the single-mode fibre. Thus, the optically trapped atoms are tightly confined in the path of fibre-guided photons for maximum overlap. Such a system is capable of writing, reading and storing quantum information and clearly has massive implications for quantum information technologies. The device presented is adaptable, scalable and highly integrated making it the ideal building block for quantum computing. Developments and modifications made to a system for producing ultracold samples of lithium-6, caesium-133 and mixtures thereof is also presented. Feshbach molecules have major applications in quantum computing, particularly in the modelling of complex many-body quantum systems. The large dipolar moment of the lithium-caesium Feshbach molecule is the largest of all the alkali dimers producing rich long-range anisotropic dipole-dipole interactions. By use of the broad Feshbach resonance situated at 834G we associate fermionic lithium-6 atoms into bosonic lithium-6-2 Feshbach molecules. Subsequent evaporative cooling drives a phase transition in the diffuse lithium gas to produce a molecular Bose-Einstein Condensate containing up to 1e4 atoms, the first to be produced in the UK. This thesis documents the construction of the quantum integrated light and matter interface (QuILMI) in its entirety from inception to realisation. An enormous amount of work has gone into the design and subsequent development of various vacuum, laser and magnetic systems that work seamlessly in tandem via a programmable control system. The system is now in a position to demonstrate to the world that atom-photon coupling on a chip is the way forward. For the lithium-caesium mixture experiment, a versatile dual-species oven has been meticulously designed, constructed and thoroughly characterised to replace one that significantly malfunctioned and harmed the experiment. The oven is capable of tuning the axial fluxes of lithium and caesium through several orders of magnitude via PID temperature controlled reservoirs. An array of fifteen 0.51mm diameter microtubes highly collimate the dual-species atomic beam such that little flux is wasted prolonging the life of both the source and the vacuum ion pumps. This source will return the system to its former glory such that the ultimate goal of realising ultracold lihtium-caesium Feshbach molecules can once again be pursued.

General Relativity (GR) has been extremely successful experimentally. However there are several reasons to consider that GR is not the complete theory of gravity. Although directly probing quantum gravity in the near future seems highly unlikely observations of the non- perturbative regime of classical gravity is improving, so any classical modification of gravity may well be testable. In this thesis we will focus on two interesting depatures from GR inspired by quantum gravity: violations of Lorentz symmetry and the weak equivalence principle. Lorentz violating (LV) gravity theories are interesting for various reasons. For example: they may have improved UV behaviour as quantum theories. Additionally testing principles which are fundamental to our understanding of nature is extremely important. We demonstrate how the causality of certain types of LV theories is realised. We then show how the relationship between two different LV theories could be used to find whether or not black holes can truly form from collapse, at least in spherical symmetry. One may be worried about whether or not LV in gravity can spoil the Lorentz invariance of matter. We generalise some known results about this problem in Horava gravity and then consider the viability of one proposal to correct this problem. Weak equivalence principle violations alter the structure of matter. By developing a simple model we demonstrate that one can maintain the weak equivalence principle in the solar system, while breaking it in high-curvature regimes. We go on to demonstrate the efficacy of the mechanism. This thesis is largely aimed at tackling questions related to the strong field regime in alternative theories of gravity: a topic of increasing interest.