The seesaw mechanism, where a hierarchy exists between the moduli of different entries of a mass mixing matrix, is a simple and theoretically attractive explanation for the observed large hierarchy between the neutral- and charged-fermion masses of the Standard Model. The simplest neutrino mass seesaw predicts that, upon diagonalisation, the physical mass states will either all be Majorana or all form pseudo-Dirac pairs. Non-minimal variants of this seesaw often generate a hybrid scenario with the physical mass states being a combination of both Majorana and pseudo-Dirac pairs. Such models often predict unique phenomenology and also allow for much lower mass scales of new physics. This thesis explores the implications such non-minimal variants can have beyond the simple generation of neutrino mass, particularly the possible role they may have in explaining the observed matter-antimatter asymmetry as well as implications for particular models of quark-lepton unification. Chapter 1 reviews the current experimental evidence for neutrino mass and discusses some possible tree-level origins. The matter-antimatter asymmetry is introduced and the conditions necessary for the dynamical generation of this observed asymmetry are reviewed. The idea of thermal leptogenesis is outlined as a simple mechanism for generating an asymmetry dynamically at an epoch between the the period of reheating and the electroweak phase transition of the early universe. Finally, the idea that quarks and leptons are related by hidden symmetries are discussed with a particular emphasis on the quark-lepton unifying Pati-Salam gauge group. In Chapter 2 we consider the leptogenesis implications for the Standard Model extended by two gauge-singlet fermions for each generation of charged lepton. We focus on the possibility of resonant scenarios without the need for inter-generational mass degeneracies and therefore do not require a possible flavour symmetry origin. The possible connection between neutrino parameters measureable in low-energy experiments and the generation of a matter-antimatter asymmetry is explored. In Chapter 3 we extend the analysis of the previous chapter and highlight how a flavour symmetry can allow for leptogenesis in a much wider region of parameter space for the extended seesaw used in \Cref{Chapter2}. The benefits of this extended seesaw, compared to the minimal seesaw scenario, when the proposed flavour symmetry is included are discussed and implications for low-energy flavour-violation experiments are explored. In Chapter 4 different possible Pati-Salam models are discussed with an emphasis on the connection between the scale of Pati-Salam breaking and the scale of heavy neutrino masses. Models allowing for the breaking scale to occur close to the electroweak scale are introduced. The dominant experimental probe of Pati-Salam is discussed and the current limits on the scale of breaking are calculated. Simple extensions of this model are proposed which both break an undesired mass degeneracy in the theory and allow for a significant reduction in the experimental limits on Pati-Salam breaking. A thorough analysis of the possible allowed parameter space in which both of these effects occur is explored and any possible connection to the symmetries of the theory is made. Chapter 5 briefly concludes.

This thesis presents a series of original studies exploring the space of neutrino-mass models, and the connection that a class of these models might have with the recently purported violations of lepton flavour universality measured in $B$-meson decays. We begin by describing and implementing an algorithm that systematises the process of building models of Majorana neutrino mass starting from effective operators that violate lepton number by two units. We use the algorithm to generate computational representations of all of the tree-level completions of the operators up to and including mass-dimension eleven, almost all of which correspond to models of radiative neutrino mass. Our study includes lepton-number-violating operators involving derivatives, updated estimates for the bounds on the new-physics scale associated with each operator, an analysis of various features of the models, and a look at some examples. Accompanying this work we also make available a searchable database containing the catalogue of neutrino-mass models, as well as the code used to find the completions. The anomalies in $B$-meson decays have known explanations through exotic scalar leptoquark fields. We add to this work by presenting a detailed phenomenological analysis of a particular scalar leptoquark model: that containing $S_{1} \sim (\mathbf{3}, \mathbf{1}, -\tfrac{1}{3})$. We find that the leptoquark can accommodate the persistent tension in the ratios $R_{D^{(*)}}$ as long as its mass is lower than approximately $\SI{10}{\TeV}$, and show that a sizeable Yukawa coupling to the right-chiral tau lepton is necessary for an acceptable explanation. Agreement with the measured $R_{D^{(*)}}$ values is mildly compromised for parameter choices addressing the tensions in the $b \to s$ transition. The leptoquark can also reconcile the predicted and measured value of the anomalous magnetic moment of the muon, and appears naturally in models of radiative neutrino mass. As a representative example, we incorporate the field into a two-loop neutrino mass model from our database. In this specific case, the structure of the neutrino-mass matrix provides enough freedom to explain the small masses of the neutrinos in the region of parameter space dictated by agreement with the anomalies in $R_{D^{(*)}}$, but not in the $b \to s$ transition. In order to address the shortcomings of the $S_{1}$ scenario, we construct a non-minimal model containing the scalar leptoquarks $S_{1}$ and $S_{3} \sim (\mathbf{3}, \mathbf{3}, -\tfrac{1}{3})$ along with a vector-like quark, necessary for lepton-number violation. We find that this new model permits a simultaneous explanation of all of the flavour anomalies in a region of parameter space that also reproduces the measured pattern of neutrino masses and mixing. A characteristic prediction of our model is a rate of muon--electron conversion in nuclei fixed by the $b \to s$ anomalies and the neutrino mass. The next generation of muon--electron conversion experiments will thus potentially discover or falsify our scenario. We also present a general overview from our model database of those minimal radiative neutrino-mass models that contain leptoquarks that are known to explain the anomalies in $R_{D^{(*)}}$ and the $b \to s$ transition. We hope that our model database can facilitate systematic analyses similar to this, perhaps on both the phenomenological and experimental fronts. We conclude by presenting a study of the diphoton decay of a scalar $\mathrm{SU}(N)$ bound state, motivated by the 2016 \SI{750}{\GeV} diphoton excess.

Glitches are sudden jumps in the spin frequency of pulsars that occur at random times and over several orders of magnitude in size. One popular theory holds that glitches are caused by differential rotation between the neutron star crust and a superfluid component in the interior. This implies that glitches can be used to study the dense nuclear matter inside neutron stars, testing a regime of physics inaccessible to present-day laboratory experiments or other electromagnetic observations. In the vortex avalanche model of pulsar glitches, the angular momentum of the superfluid is determined by the configuration of an array of quantized vortices which pin to impurities in the interior. As the star spins down, individual vortices unpin and move outwards, triggering unpinning in other nearby vortices leading to an avalanche. The angular momentum lost by the vortices as they move outward is transferred to the crust, which causes it to spin up. This thesis tests the superfluid model of pulsar glitches using hydrodynamic simulations of glitch recovery, statistical analysis of astronomical glitch data and N-body point vortex simulations of avalanches in an idealised neutron star model. Following a glitch, pulsars often have a lengthy recovery period of weeks to months, which is a key piece of evidence for the presence of a superfluid phase inside neutron stars. We perform simulations of glitch recovery using a pseudo-spectral Navier-Stokes-like solver. We model a neutron star as a two component superfluid consisting of a viscous proton-electron plasma and an inviscid superfluid neutron condensate in a spherical Couette geometry. The two fluid components are coupled through mutual friction. We prepare the system in a state of differential rotation between the core and the outer crust and examine the response of the outer boundary to glitches induced by instantaneously changing the angular velocity of the boundaries and by recoupling the fluid interior. We find that with strong mutual friction the characteristic glitch recovery time scale decreases by as much as a factor of three. For glitches originating in the fluid, strong mutual friction decreases the maximum spin up by a factor of up to five. These effects may be partially responsible for the diversity of glitch recoveries observed in the pulsar population, which vary from rapid, complete recoveries to slow partial recoveries or step changes in the spin frequency with no observed change in the spin down rate. The strength of mutual friction depends on where in the star a superfluid phase exists, so these results may allow future observations to constrain the star's internal structure. The vortex avalanche model of glitches is similar to other non-equilibrium systems in nature such as sandpiles, earthquakes and solar flares. Such systems are often studied in the paradigm of self-organized criticality (SOC), a hallmark of which is scale invariant size probability density functions (PDFs) and exponential waiting time PDFs. We perform a statistical study of the size and waiting time PDFs for the five most prolific glitching pulsars using the non-parametric kernel density estimator. This work complements previous parametric studies of glitches, which typically fit the PDFs to known distributions such as power laws, Gaussian or log-normal distributions. Two objects, PSR J1740-3015 and the Crab pulsar PSR J0534+2200, appear to have exponential waiting time PDFs and scale-invariant size PDFs over several decades. Two other objects, PSR J0537-6910 and the Vela pulsar PSR J0835-4510 have quasiperiodic size and waiting time PDFs, typical of fast-driven SOC systems. One object, PSR J1341-6220, appears to exhibit hybrid behaviour. We test the ability of the kernel density estimator to resolve multimodality in synthetic data drawn from a composite Gaussian distribution (which is qualitatively similar to the waiting time PDF in J1341-6220), and find that the small number of glitches observed in this object (N = 23) makes confirmation of multimodality in the PDFs difficult. In order to study the non-equilibrium dynamics of the vortex avalanche theory of glitches, it is useful to have an idealised model which can make falsifiable predictions about the properties of glitches, such as PDFs of sizes and waiting times, correlations between these observables, and the dependence of the PDFs on the internal parameters of the model. Previous work with Gross-Pitaevskii simulations has been unable to study systems larger than ~100 vortices, far from the ~10^18 vortices in neutron stars. With such small numbers of vortices, it is impossible to resolve the dynamics over multiple orders of magnitude. We develop a mathematical model for simulating the motion of point vortices in two dimensions under the influence of deceleration, dissipation, and pinning. We describe a numerical solver for this model, which uses an N-body method to compute the vortex velocities and an adaptive time step scheme for time evolution. We present the results of numerical experiments validating the method, including stability of a vortex ring and dissipative formation of an Abrikosov array. We then perform simulations of 1000-5000 vortices with a wide range of values for the strengths of dissipation and pinning, pinning site density and deceleration of the container. Vortex avalanches occur routinely in the N-body simulations, when chains of unpinning events are triggered collectively by vortex-vortex repulsion, consistent with previous, smaller scale studies using the Gross-Pitaevskii equation. The PDFs of the avalanche sizes and waiting times are consistent with both exponential and lognormal distributions. We find weak cross-correlations between glitch sizes and waiting times. These correlations are consistent with astronomical data and meta-models of pulsar glitch activity as a state-dependent Poisson process or a Brownian stress-accumulation process, and inconsistent with another popular alternative, a threshold-triggered stress-release model with a single, global stress reservoir. The spatial distribution of the effective stress within the simulation volume is analysed before and after a glitch.We find that stress is distributed homogeneously throughout the system and remains near the critical threshold both before and after glitches. This implies that there is no 'memory' in the system; glitches do not significantly reduce the global or local stress. This is consistent with the lack of strong cross-and-auto correlations between glitch sizes and waiting times in the simulations and pulsar data.

We employ the newly developed Matrix Product State (MPS) formalism to simulate two problems in the context of quantum information processing. One is the Boson sampling problem, the other is the ground state energy density of an n-qubit Hamiltonian. We find that the MPS representation of the Boson sampling problem is inefficient due to large entan- glement as the number of photons increases. In the context of adiabatic quantum computing (AQC), MPS is used to find the first four moments of an n-qubit Hamiltonian to approximate the ground state energy density of the Hamiltonian. We show an advantage of using the first-four-moment method over the conventional adiabatic procedure. Future work around AQC using MPS is discussed.

Biological discovery is fuelled by technological advances. As a new process is developed, a period of exploration tests the waters to uncover what the novel technology can reveal. This thesis presents the application of quantum sensing with negatively-charged nitrogen vacancy (NV) centres in diamond to real biological systems and questions. NV sensing provides a means to probe systems, including biosystems, in ways unavailable with other techniques. This is most evident in the NV’s magnetic sensitivity, along with a collection of attributes that lend it to biological settings. Many questions about biomagnetism remain unanswered, and the advent NV sensing affords a new avenue to explore these questions. In this thesis, we begin by establishing the techniques and capabilities of NV magnetic imaging in diamond. An introduction to magnetometry precedes a description of diamond, the properties of the NV centre, and quantum measurement protocols. We then dive into an animal model of iron biomineralisation, a sea mollusc with extraordinary teeth. Biomineralisation is an area of current interest that has previously received little attention from the angle of its intrinsic magnetic properties. Next, we see how nitrogen vacancy sensing can be applied to the improvement of magnetic tools used in the biosciences. These tools are seeing an explosion of new activity across multiple disciplines, so ways to evaluate them will prove valuable. Then, we examine the enigmatic mechanism behind animal magnetoreception. A remarkable sense known to be possessed by many disparate animal species, magnetoreception remains a near complete mystery. Finally, we consider the challenges and limitations of diamond-based temperature sensing in biological systems. This interdisciplinary endeavour has brought about exciting results including the first subcellular magnetic profiling of a eukaryotic system, vector magnetic images of developing biominerals, new protocols for the assessment of magnetic materials and avenues for new bioassays, and a window to a recently-discovered organelle with a suggested role in animal magnetoreception. With the current trajectory of quantum sensing with NV centres in diamond, the future for biological discovery looks bright.

Understanding the array of physical processes that have shaped galaxy assembly remains one of the most fundamental pursuits in astrophysics. Gas in galaxies is enriched with heavy elements via stellar nucleosynthesis, but chemical abundances (``metallicity'') are also shaped by galaxy-scale processes including gas accretion, feedback-driven outflows, radial gas flows, interactions, and mergers. Metallicity measurements therefore afford one of our most powerful observational probes of galaxy evolution. In this thesis I explore the performance of observational methods for constraining (i) gas-phase metallicity in galaxies, and (ii) host dark matter halo masses of galaxies; the latter of which is critical to the physics of gas flows due to its contribution to the gravitational potential well of galaxies. A particular focus is the improved understanding of systematic uncertainties near instrumental limits, which will be vital to maximise the impact of surveys conducted with future facilities. Galaxy clustering is an efficient approach for drawing statistical connections between galaxies and their host dark matter haloes, however traditional methods are challenging to apply at z > 2 where imaging survey volumes are limited. I instead apply a counts-in-cell approach to photometric z ~ 2 candidates from a random-pointing Hubble Space Telescope survey, showing mean counts of N > ~5 per field are capable of constraining the large scale galaxy bias. The James Webb Space Telescope will achieve comparable number counts out to z ~ 8, and thus a similar JWST survey could place novel constraints on the halo masses of galaxies in the epoch of reionization. Global metallicities in low-mass galaxies afford important constraints on the impact of feedback-driven outflows on galaxy evolution. However at high-z, obtaining the requisite emission line measurements is observationally challenging. I use Keck/MOSFIRE spectroscopy to explore prospects for extending z ~ 1 - 2 metallicity measurements to lower masses. I find the dominant source of uncertainty arises from reduced number of emission lines as opposed to lower signal-to-noise, even at the detection limit. JWST/NIRSpec will revolutionise high-z metallicity studies due to the large suites of emission lines it will be able to assemble. Electron temperatures (T_e) measured with auroral lines are an important baseline in metallicity studies. However the faintness of auroral lines has hitherto limited spatially resolved T_e studies. I report two separate studies based on mapping auroral lines in integral-field spectroscopy (IFS) of low-z galaxies. Measurements of auroral lines in the SAMI Galaxy Survey afford new insights into the effects of ionisation parameter variations on recovered metallicity gradients. Applying these principles to Keck/KCWI IFS data of an edge-on disk galaxy, I measure an extra-planar temperature gradient and present preliminary evidence for extra-planar metallicity variations.

The processing of spatial information, including images, is fundamental in modern scientific, industrial and medical applications. Some imaging techniques rely on amplitude information contained in a wavefield and permit conversion of optical information into electronic signals through conventional integrated photodetector technology and subsequent digital processing. The ever increasing complexity and volume of data that often needs to be processed in real-time and with low energy consumption in applications such as satellite imagery, autonomous vehicles or object and face recognition pushes current electronic systems to its limits. Other situations utilize the extraction of polarization or phase information from a wavefield which commonly requires the use of optical image processing technology. The visualization of phase information underpins for example widely employed techniques to enhance image contrast in live biological cells. Conventional optical processing approaches, however, typically involve expensive and bulk-optical components thereby limiting their potential to be involved in next-generation compact optical systems. These constraints on current electronic and optical processing technology require the development of new solution approaches. Ultra-compact, analogue optical solutions that enable real-time processing of spatial information carry potential to circumvent conversion of optical to electronic signals and the associated digital computation while simultaneously avoiding bulk-optical components. The significant progress in micro- and nanofabrication over the last decades has enabled researchers to create artificial materials with unprecedented optical characteristics including photonic crystals, thin-film systems and optical metasurfaces. Recently these systems have gained considerable scientific attention for the implementation of analogue spatial computation devices and have been applied to all-optically perform mathematical operations including differentiation and integration on optical images. In particular approaches that enable accessing and manipulating the Fourier content of a wavefield in the object-plane carry vast potential for the development of flat optical image processing solutions. The main objective of this work is to further our understanding of ultra-compact all-optical image processing in general, and to develop specific implementation approaches utilizing nanophotonic structures. Here the conception, modelling, fabrication and characterization of three fundamentally different approaches to nanophotonic image processing in the object plane are presented for the first time. Firstly, metal-insulator-metal thin-film absorbers are investigated for the first time as reflective image processing devices. Secondly, the excitation of subradiant modes on plasmonic trimer metasurfaces is exploited to perform all-optical spatial frequency filtering in reflection. Finally, plasmonic resonant waveguide gratings are investigated as compact transmitting spatial frequency filters. The implemented solutions are applied as high-pass spatial frequency filters to demonstrate all-optical edge-detection in amplitude images and the visualization of phase gradients in optical wavefields. Furthermore proof-of-concept application of the investigated structures to image processing of biological samples is demonstrated. The results of this thesis contribute to the advancement of our understanding of nanophotonic systems for the processing of spatial information and demonstrate their significant potential to be integrated in next-generation optical systems.

Quantum computers are set to revolutionise technology by harnessing the immense promise of quantum mechanics, the law governing nature on the atomic scale, to enable a dramatically increased efficiency for certain algorithms over their classical counterparts. By storing and manipulating information on quantum bits (qubits), which can exist in a superposition of 0 and 1 at the same time and can be entangled with each other, instead of classical bits, which are strictly 0 or 1, certain problems that are intractable with classical computation can be solved. To realise a qubit, a quantum system that exists in two or more states, such as a spin in a magnetic field, is required. Group V donors in silicon (Si) are promising qubit candidates that can store quantum information in both the spin of the donor nucleus and the donor electron that it binds by the Coulomb potential. Si offers an ideal platform due to its isotopic composition of predominantly spin-zero nuclei (over 92% is 28Si with nuclear spin I=0), that can provide a noise-free host lattice, and the wealth of knowledge accumulated in the microelectronics industry. The most versatile method for introducing donors in Si is ion implantation, a foundational technique of the information technology industry that has already demonstrated the production of long-lived phosphorus (P) donor qubits. This method is explored in this thesis. The bismuth (Bi) donor offers some useful properties for quantum devices, such as an increased quantum memory, clock transitions and the potential to couple to superconducting flux qubits. To fabricate a quantum device that employs Bi, it is necessary to implant and activate a Bi donor in Si. Here, the optimum implantation and thermal annealing strategy is determined to maximise the operational yield of near-surface Bi donor qubits by repairing the Si crystal damage and electrically activating the donor, evidenced by the measurement of Bi donor electron spin resonance. A further critical issue in donor qubit fabrication is the depletion of the nuclear spin-1/2 29Si isotope to extend coherence times, which would be beneficial to be performed routinely. Accordingly, a method of isotopically enriching a surface layer of natural Si via sputtering during the high fluence implantation of 28Si- ions was developed. This technique increases the accessibility of producing spin-free 28Si material by requiring only a conventional ion implanter and naturally abundant sources. The successful recrystallisation of this 28Si layer and the demonstration of increased coherence times for implanted P donors make this a promising technique for integrating into the fabrication of implanted donor qubits. Finally, the measurement of the full extent of the 29Si depletion on the coherence time requires a low concentration of donors implanted into this ~100 nm thick surface layer of 28Si. Therefore,a high sensitivity technique capable of probing a small number of spins is essential. This challenge is addressed by the design and implementation of a low-temperature electrically detected magnetic resonance (EDMR) system, capable of measuring spin transitions of donor electrons in Si with a sensitivity at least 5 orders of magnitude greater than for conventional electron spin resonance systems. In future, this will allow for the coherence times of donors implanted into our enriched 28Si layers to be determined from the linewidth of EDMR signals. This thesis lays the foundations for exploiting Bi donor clock transitions in qubit devices and addresses the challenge of providing an isotopically enriched 28Si matrix for donor qubits that is shown to extend qubit coherence times and thus makes progress towards the scalable fabrication of a donor spin quantum computer.

Coulomb interactions within charged particle bunches manifest themselves through microscopic statistical Coulomb effects and macroscopic Coulomb explosion, also known as space-charge expansion. Coulomb explosion can lead to unwanted increases in the phase-space density or emittance of the source, which reduces overall focusability and brightness. Therefore, the ability to control, suppress and potentially eliminate space-charge-induced emittance growth in charged particle beams is of critical importance for applications in high-energy accelerator injection, high-brightness X-ray sources, electron and ion microscopy, and ultrafast electron diffraction (UED). The capacity to perform single-shot UED and coherent diffractive imaging experiments of protein membranes and biological samples is of particular interest; the "holy grail" of structure determination techniques. Such an experiment requires high bunch charge and short pulse durations, conditions that result in severe Coulomb explosion. Conventional electron sources cannot simultaneously achieve the high brightness and high coherence properties required to dynamically image biomolecules, due to limitations imposed by Coulomb effects. Recently, a new generation of Cold Atom Electron and Ion Sources (CAEISs) have been developed and show promise in this regard, utilising low temperature to generate high brightness and coherence. The Melbourne CAEIS produces electron or ion bunches via two-colour near threshold photoionisation of laser-cooled rubidium atoms in a magneto-optical trap. The photoionisation laser can be tuned to excite electrons to the continuum with almost no excess energy, resulting in electron and ion bunch temperatures of approximately 10 K and 1 mK respectively, orders of magnitude lower than that of conventional field emission or photocathode sources. Without obfuscation from thermal diffusion, space-charged-induced effects that evolve within a bunch can be measured and alleviated by carefully tailoring the initial density profile. Specifically, the ideal bunch is a three-dimensional (3D) uniform density ellipsoid of charge, which exhibits linear and therefore reversible Coulomb expansion and minimal emittance growth under acceleration and propagation. Such objects were first realised for radio frequency (rf) photocathode sources, whereby a prompt, half-spherical radial laser intensity distribution and strong accelerating field were used to generate and extract a pancake electron bunch from the cathode surface, which automatically evolves into a 3D uniform ellipsoidal bunch, provided certain criteria are met. This formalism is adapted to the Melbourne CAEIS using a spatial light modulator for transverse laser beam shaping to create ion bunches that undergo linear space-charge expansion. Nanosecond ion bunches are investigated as they exhibit strong space-charge effects that are analogous to picosecond electron dynamics, on time-scales relevant for UED. An experimental framework is introduced to allow comparisons between CAEIS-generated half-spherical bunches and other common bunch distributions, namely Gaussian, flat-topped, and conical. By measuring Coulomb expansion for the chosen bunch shapes as a function of increasing density, growth factors are calculated and linear space-charge expansion is verified in a CAEIS for the first time. Particle tracking simulations are used to calculate emittance and emittance growth of cold, shaped bunches, with comparisons made to a thermal source. Transverse bunch focusing experiments are also presented which demonstrate suppression of space-charge-induced emittance growth via bunch shaping. By simulating an rf cavity in the CAEIS beamline for longitudinal bunch compression, 3D reversal of Coulomb explosion is explored and also confirms emittance suppression and brightness enhancement for particular shaped bunches. The concept, design and performance of a novel cateye external cavity diode laser for continuous CAEIS development is also described in this work.

Semi-analytic models play an important role in modelling the epoch of reionisation. This thesis presents three studies that are related to this topic. First, we measure clustering segregation with both UV-luminosity and stellar mass at z > 4, which is then compared with predictions from the Meraxes semi-analytic model. Our results suggest that the dependence of clustering strength on UV-luminosity is stronger than stellar mass, indicating that compared with stellar mass, UV-luminosity is more tightly correlated with halo mass. Secondly, we investigate dust extinction in the early Universe. Our method utilises the Meraxes semi-analytic model to produce intrinsic galaxy luminosity and adopts parametric relations to estimate dust extinction. A novelty of our approach is that intrinsic luminosity and dust extinction are determined simultaneously by calibrating both galaxy formation and dust models against only UV observations. Our results suggest that there is a factor of two systematic error in the estimations of the cosmic star formation rate density based on the dust law in the local Universe. Finally, we present a method to augment N-body simulations using a Monte Carlo algorithm, which increases the mass resolution of the simulations. The results can be used by semi-analytic models of reionisation to overcome the challenge that convergent predictions of the reionisation history require both high mass resolution and large simulation volume. The effectiveness of our method is tested using a high resolution small volume N-body simulation.

The controlled use of coherent radiation has led to the development of a wide range of imaging methods in which aspects of the phase are enhanced through diffraction and propagation. A mathematical description of the propagation of light allows us to determine the properties of an optical wavefield in any plane. When a sample is illuminated with coherent planar illumination and its diffracted wavefield is recorded in the far-field of propagation, a direct inverse calculation of the phase can be quickly performed through computational means – the fast Fourier transform. Algorithmic processing is required, however, because only the intensity of the diffracted wavefield can be recorded. To determine structural information about the sample, some other information must be known about the experimental system. What is known, and how it is processed computationally, has led to the development and successful application of a broad spectrum of phase reconstruction iterative algorithms. Vortices in lightfields have a helical structure to their wavefront, at the core of which exists, necessarily, a screw-discontinuity to their phase. They have a characteristic intensity distribution comprising a radially symmetric bright ring around a dark core which, for either handedness of the rotation of the vortex, appears identical. Observation of a vortex is, therefore, ambiguous in its ability to determine its true direction of rotation. The ubiquitous presence of vortices in all lightfields hinder the success of phase reconstruction methods based on planar illumination and, if successful, render any reconstruction of the phase non-unique, due to the ambiguity associated to their helicity. The presence of a controlled spherical phase distortion can break the symmetry of the appearance of the vortices and, hence, remove the ambiguity from the system and drive algorithms to a solution. For the pathological case of an on-axis vortex, however, spherical distortion will not break the radial symmetry. The astigmatic phase retrieval method separates the spherical distortion into cylindrical distortion in two orthogonal directions. This form of phase distortion breaks the symmetry of a vortex allowing a unique determination of the phase. The incorporation of such use of cylindrical distortion into an iterative phase reconstruction algorithm forms the basis for the astigmatic phase retrieval (APR) method. Presented in this thesis is the creation and propagation of lightfields with helical wavefronts, produced through simulation and experiment. Observation of the effects of cylindrical distortion on vortices is explored in detail, particularly for split high-charge vortices where their positions can inform the type and strength of the applied phase distortion. Experimentally, onaxis vortices are created and distorted for the purposes of astigmatic phase retrieval in both visible light and X-ray wavefields. This thesis presents the first experimental demonstration of the astigmatic phase retrieval (APR) method, successfully applied optically with a simple test sample. The method is also applied to lightfields with helical wavefronts. The successful unambiguous reconstruction of on-axis chargeone and charge-two visible light vortices are presented, which is the first experimental demonstration on the unique phase reconstruction of an on-axis vortex from intensity measurements alone. Experiments are then performed to apply the method to vortices created in X-ray wavefields. The parameters of the experiment and the data have not, however, allowed for a successful reconstruction in this case. It is demonstrated through extensive simulation analysis that the APR method is a fast and robust imaging method. It is also shown that, through observation of the error metric, experimental parameters can be corrected or even determined, making the method successful even if there is no a priori knowledge of the experimental system. The application of the APR method as a general imaging technique for use in high-resolution X-ray diffraction experiments is, therefore, is a logical extension of the work of this thesis.

This thesis present the result of four experimental projects, that revolve around the practical aspects of using NV centers for quantum applications. The core of the this work deals with the coherence time of NV centers and how it is affected by damage introduced into the diamond lattice by ion implantation where we have discovered that while the emission of the NV center is sensitive to the damage the coherence time is not. The other topics of this work cover a novel method to deposit isolated nano diamond using aerosols and a method to secure the nano diamonds into silicon substrates using self-assembled mono layers. Finally, the work concludes with a proposal to use the magnetic field produced by spin vortices to increase the coherence time of NV centers where some preliminary result of the spin vortices fabrication are presented.