Unconventional superconductivity has experienced tremendous growth in research interest and activity ever since the discovery of high-Tc superconductors. The variety and rich phenomenology of superconducting phases are promising for future device applications and technological advancement. Topological superconductivity constitutes another class of unconventional superconductors which are sought after for their applications as a material platform for fault-tolerant quantum computing. Until now, however, only a handful of candidate materials are known, and the lack of understanding of what exactly drives those phases represents a major challenge. There is no "recipe" yet for how to systematically search for topological superconductors. Similarly, there is no widely accepted theory that explains the microscopic mechanisms behind unconventional superconductors in general. The presented work extends the weak coupling renormalization group method, which we employ to provide a systematic study of unconventional superconductivity in two dimensional lattice systems. One of the major goals is to find out which of the possible "ingredients" - lattice symmetries, longer-range effects, multi-orbital effects, topology of the non-interacting system, and spin-orbit interactions - can promote the formation of topological superconducting states. We apply our method to paradigmatic lattice models and use our results for benchmarking. We then study an application to real materials: a monolayer of tin adatoms on a silicon substrate and a comparison of the LNO/LAO heterostructure with a barium copper oxide superconductor. After that, we continue with an investigation of the effect of Rashba-spin orbit coupling, which breaks inversion symmetry and thus causes mixing of spin-singlet and spin-triplet states, and a study on the effect of different topologies of the non-interacting system on the superconducting state. One of the overarching conclusions is that strong longer-range effects, like longer-ranged hopping and nearest-neighbor interactions, tend to benefit topological superconductivity. Furthermore, lattices with hexagonal symmetry seem to be especially beneficial for topological superconducting states with (relatively) high critical temperature.

Intense laser-atom interactions are of research interest primarily due to their potential as a table-top source of coherent short-wavelength radiation. The production of this radiation, known as High Harmonic Generation (HHG), is driven by the electric field of the laser and depends on electron motion at timescales significantly shorter than the oscillation period of the field. The response of an atom is highly-nonlinear and can be modelled accurately only by the numerical solution Time-Dependent Schrodinger Equation (TDSE), a procedure which is computationally expensive. Such modelling is essential for the fine tuning or optimisation of these light sources. In this thesis, a novel method of performing TDSE integration is presented, based on the Stabilised Bi-Conjugate Gradient method (BiCG-STAB). This is an iterative procedure which allows substantial flexibility in the representation of the atomic wavefunction and the Hamiltonian operator. A requirement of this method is that the equations are suitably preconditioned to ensure smooth convergence of the algorithm. It is shown that the ability of this method to incorporate higher-order representations of the spatial and temporal derivatives with minimal cost is particularly advantageous. This method is shown to be faster than established methods, most notably in the computationally difficult cases of high laser intensity and long wavelength, or when the demands of accuracy are high. Using this method, the dynamics of atoms in intense laser fields are studied in a variety of contexts. The photoelectron spectra produced in interactions with atomic hydrogen are investigated in great detail as a function of laser pulse parameters. This is highly relevant to the use of photoelectron spectra as a calibration standard for laser systems. HHG in two colour fields is also investigated in two projects: the first of these examines selection rules of harmonic emission from two femtosecond pulses of incommensurate frequencies; the second project assesses the viability of enhancement of attosecond pulse generation through the introduction of a third harmonic field with a tunable phase. It is found that the production of relevant harmonics can be enhanced when the third harmonic is adjusted to boost ionisation at favourable parts of the cycle. Finally, a means of visualising and interpreting the output of TDSE simulations is investigated through the use of the Wigner quasi-probability distribution. This provides a phase space depiction of the evolution of atoms in strong laser fields that allows for direct comparison to semiclassical models. This builds upon previous applications of Wigner methods to strong field interactions by application to three-dimensional wavefunctions.

The last 20 years have heralded the synthesis of Bose-Einstein condensates (BECs) of elements with large magnetic dipole moments, such as chromium, erbium and dysprosium, polarised by a magnetic field. These dipolar BECs experience both the dipole-dipole interaction (DDI) and a short-ranged, effectively isotropic interaction, rendering them a robust platform for studying the interplay of such interactions in many-body quantum systems. Thus, it is useful to be able to independently control the two interaction strengths. In this context, it has long been known that the temporal average of the DDI arising from a rapidly rotating magnetic field is simply that of a static field with an interaction strength dependent on the angle between the field and its rotation vector. However, while numerous theoretical studies assumed that the DDI may effectively be tuned by rapidly rotating the dipole polarisation, this assumption had not been rigourously examined when the author’s candidature commenced. In this thesis, we investigate harmonically trapped dipolar BECs in time-dependent magnetic fields via an effective mean-field theory, the dipolar Gross-Pitaevskii equation (GPE). This involves semi-analytically identifying the stationary states in the interaction–dominated Thomas-Fermi (TF) limit and then solving for the corresponding collective modes of the BEC to identify when it is dynamically unstable against the exponential growth of a mode. Initially, we study a nondipolar BEC in a tilted rotating harmonic trap and uncover a dynamical instability above a certain critical rotation frequency that is lower than the transverse trap frequency. Complementary numerical solutions of the GPE demonstrate that this instability results in vortex nucleation and, ultimately, a vortex lattice embedded in a tilted background density. This informs our analysis of a statically harmonically trapped dipolar BEC in a rotating magnetic field. Regardless of the field tilting, we find that at sufficiently high rotation frequencies, the stationary states closely mimic those of the corresponding time-averaged DDI. However, a critical rotation frequency is also uncovered, for any nonzero tilt angle, above which the stationary states are dynamically unstable. In the limit where the field is orthogonal to its rotation axis, these predictions are then compared with numerical simulations of the dipolar GPE. If the rotation frequency exceeds the transverse trap frequency, we find that the dynamical instability induces the turbulent decay of the stationary state, which may explain the unexpectedly short BEC lifetime observed in recent experimental investigations of DDI time-averaging. Conversely, rotation below the transverse trap frequency causes vortex nucleation – as yet unobserved in dipolar BECs – and ultimately a vortex lattice. Finally, a variational formalism for the TF dynamics of dipolar BECs is developed. This allows us to demonstrate the excellent agreement of the dynamics predicted by the time-averaged DDI with those influenced by a rapidly rotating field. Furthermore, we find that large-angle oscillations of the dipole polarisation induces the nonlinear coupling of quadratic collective modes, a phenomenon of long-standing interest. Together, these results suggest that directly rotating the dipole polarisation represents a simple, yet powerful, method to control and induce novel phenomena in dipolar BECs.

The understanding of electrogenic cells and their networks in vitro plays a major role in the development of therapies targeting maladies of the cardiovascular and nervous systems. Continued advancement of this understanding relies on the use of tools which can measure electrical potentials with ever-increasing spatio-temporal resolution and scale. However, present voltage imaging technologies cannot simultaneously achieve sub-cellular resolution while recording over whole-network spatio-temporal scales, which leads to incomplete descriptions of network function and dysfunction. In this thesis, we report on the early stage development of a fundamentally new tool for quantitative voltage imaging which can overcome the physical limitations of the present state of the art. The central goal of the work is to investigate the extent to which charge-state transitions of fluorescent point defects in wide-bandgap semiconducting materials can be exploited to image bio-electrical activity in vitro. Here, we use the nitrogen-vacancy centre in diamond as an experimental platform for exploring this topic. We describe the design, fabrication, and testing of a novel voltage imaging chip technology which relies on optically detecting the charge-state conversion of near-surface nitrogen-vacancy ensembles in response to electrical potentials in solution. These ensembles are localised within nanoscale diamond p-n junctions and embedded within the tips of diamond nanopillars, which we refer to as ‘optrodes’ in analogy with standard electrodes. Through several generations of diamond optrode arrays, voltage sensitivities are increased by more than three orders of magnitude. The work culminates in a device possessing a voltage sensitivity only one order of magnitude less than that of commercial high-density multi-electrode array systems, and we calculate that the sensitivities of future devices can be improved beyond that of state-of-the-art technologies. Concurrent to the development of physical devices, a nonlinear Poisson solver was constructed to study the effects of dopant concentrations and depth distributions, as well as the effects of diamond surface defects, on voltage sensing performance. Informed by this modelling, a new method for precisely tuning the surface chemistry of diamond for optimal charge-state sensing was developed, enabling the fabrication of a device containing high-density nitrogen-vacancy ensembles stabilised entirely in the neutral and positive charge-states. To our knowledge, this is the first ever realisation of high-density nitrogen-vacancy ensembles exclusively comprised of positive and neutrally-charged defects. The thesis concludes with a discussion of known and possible pathways for increasing the performance of future devices. In addition, we highlight some possible directions for fundamental research which may help to further advance this emerging technology. This work establishes the feasibility of using charge-sensitive fluorescent defects in diamond for all-optical imaging of electrical potentials with both high spatial resolution and over large spatial and temporal scales.

Biochemical processes are conducted by interactions of individual molecules that comprise cells. It is the transient physical shape of proteins that dictates their specific functionality. However, imaging individual instances of single molecular structures is one of the notable challenges in structural biology. Presently available protein structure reconstruction techniques, Nuclear Magnetic Resonance (NMR) spectroscopy, X-ray crystallography and cryogenic Electron microscopy (cryo-EM), cannot provide images of individual molecules. Despite their power and their complementary capabilities, said techniques produce only average molecular information. They achieve this by sampling large ensembles of molecules in nearly identical conformational states. As a result, individual instances of a generic, inhomogeneous or unstable atomic structures presently remain beyond reach. We seek to address this problem in a novel way by leveraging quantum technologies. In quantum computing, qubits are usually arranged in grids and coupled to one another in a highly organised manner. However, what if a qubit was coupled to an organic cluster of nuclear spins instead, e.g. that of a single molecule? What can be done with such a system in the context of quantum control and 3D imaging of individual molecular systems? What are its ultimate limits and possibilities? We explore those questions in stages throughout the chapters of this thesis. We begin in Chapter 2 by investigating dipole-dipole interactions present between the nuclear spins in a target molecule, on one side, and between an electron-spin based qubit and each of the nuclear target spins on the other. We consider the Nitrogen Vacancy (NV) centre in diamond as an example of a suitable qubit with an active community interest as a biocompatible nano-magnetometer. Our intention is to lay down foundations that will help us advance from magnetometry to 3D molecular imaging. Our inspiration comes from drawing parallels between the single molecule sensing in the qubit-target system and the clinical Magnetic Resonance Imaging (MRI). An MRI machine directly images a single, specific sample in its native state regardless of its characteristics. That is precisely what we would like to achieve on the molecular level. In Chapter 3, we develop a framework that allows a spin qubit to serve as a platform for 3D atomic imaging of molecules with Angstrom resolution. It uses an electron spin qubit simultaneously as a detector and as a gradient field provider for MRI-style imaging. We develop a theoretical quantum control methodology that allows dipole-dipole decoupling sequences used in solid-state NMR to be interleaved with the gradient field provided by the qubit. In Chapter 4, we propose group-V donors in silicon as a novel qubit platform for bioimaging. Actively researched for quantum computing purposes, such qubits have not been considered in the biological context. A prime example of this class of qubits is the phosphorus donor in silicon (Si:P). We show how its specific set of properties, including long coherence times, large wave function and low operational temperatures can be leveraged for the purposes of atomic level imaging. Finalising the work in Chapter 5, we simulate the imaging process for one transmembrane protein of the influenza virus embedded in a lipid membrane. This demonstration highlights the potential of silicon spin qubits in the future development of in situ single molecule imaging at sub-Angstrom resolution.

Quantum Computing offers the potential to efficiently solve problems for which there are no known, efficient classical solutions such as factoring of semi-prime numbers and simulation of quantum- mechanical systems. This work considers a novel moments-based adaptation of the Variational Quantum Eigensolver (VQE), one of the leading candidates for demonstrating quantum supremacy. The method for improving the estimated ground state energy of a quantum system, obtained using the Variational Quantum Eigensolver, is presented and tested for Heisenberg model systems using IBM’s superconducting quantum devices. The method is based on the application of a Lanczos expansion technique based on the computation of Hamiltonian moments and is found to offer better accuracy than conventional VQE for most cases considered, allowing for a simpler trial state and offsetting the effects of noise.

Advances in theoretical and computational techniques for advancing concepts in nanophotonics along with major development in nanofabrication technologies has enable the realization of nanoscale optical device with unprecedented ability to control light such as plasmonic metasurface. Fabrication of plasmonic devices, however, has long been relying on conventional lithography technique such as electron beam lithography (EBL), focused ion beam (FIB) milling and photolithography (PL). While these lithography techniques have enable construction of sub-wavelengths nanostructures, their reliance on the interaction between charged particles or light beam with polymer resist during pattern writing process require intricate control systems and usually require high operating and maintenance cost. In fact, for FIB and EBL, the writing time can be very slow depending on the pattern area. These approaches, therefore, are unsuitable for industrial scale production thus hindering commercial uptake of metasurfaces. Therefore, there is a need for an alternative low-cost, high-throughput nano-manufacturing approach to overcome the bottleneck in conventional lithography methods. With this motivation in mind, this thesis focused on utilizing the nanoimprint lithography (NIL) technique for fabrication of the designated plasmonic device. NIL uses pattern transfer approach whereby a predefined pattern on a mould is used to replicate the pattern onto another surface. NIL offers scalability and high-throughput large area manufacturing of nanostructures. In this thesis, the versatility and capability of NIL for producing plasmonic device, particularly plasmonic colours, with a potential of scalability is investigated. This includes the investigation of the dynamic flow of the resist during the nanoimprinting process through various process parameters. With this information, it will be shown that NIL is capable of producing multi height, grayscale-like structures through a careful control of the flow of the resist, without relying on control of charged particle or light beams. This novel technique was then utilised as a method to print the plasmonic colouration device, with ability of controlling the hue and saturation of the resulting colours via tuning of the vertical gap size of the structure. Additionally, an investigation of multispectral, polarisation-selective iridescence plasmonic colour will also be shown in this thesis. This was achieved via the elongation of the spatial dimension of plasmonic structure which results in multiple resonances in both visible and infrared region of the spectrum. Such multispectral system will be very useful especially for optical security device. Finally, a novel plasmonic colour designed to preserve the vividness of the resulting colour under unpolarised ambient lighting condition will be demonstrated in this thesis. This involves production of polarization-independent plasmonic structure featuring symmetric cross structures. It will be shown that this device produced excellent colours with preserved hue and vividness, regardless of polarization state of light

X-ray Absorption Spectroscopy (XAS) is the study of quantum interference of the photoelectron emitted upon ionisation of an absorbing atom by an incident x-ray. XAS is one of the most popular techniques of synchrotron science and most modern synchrotrons have several dedicated beamlines for this purpose. The overwhelming majority of research in this field measures secondary fluorescence photons emitted by the sample of interest. This type of measurement suffers from the dominant systematic error of self-absorption of the fluorescence photon which compromises accuracy, analysis and insight. This work presents a novel self-consistent methodology to correct for this systematic error. These results represent an enormous improvement over any previous attempt to correct for this systematic error. This method (and accompanying software package) can be applied to any fluorescence XAS data set leading to a widely-applicable general solution. XAS is an invaluable tool in the interpretation of much organometallic chemical physics including stereochemistry and quantum structure. Ferrocene is arguably the archetypal organometallic. The 1973 Nobel Prize in Chemistry was awarded on the basis of its discovery and for the identification of its extraordinary nanostructure. Subsequently, its nanostructure has been the subject of dozens of experimental investigations using widely-ranging techniques and a continued source of debate for over 6 decades since its discovery. I have successfully investigated the nanostructure of the isolated ferrocene molecule using a novel combination of Fourier Transform Infrared (FTIR) spectra processing techniques. Detailed analysis of experimental data was undertaken using modern Density Functional Theory (DFT) calculations for high-accuracy hypothesis testing. In this way, the most compelling evidence yet of the existence of the ‘eclipsed’ conformer of ferrocene is presented.

The central thread of this thesis describes the testing and commissioning of the optical fibre beam-loss monitor (oBLM) for use at the Australian Synchrotron. The four 125 m long silica fibres that form the sensitive detectors of the oBLM are installed on the Aus- tralian Synchrotron and provide complete baseline coverage of the accelerator, from the electron gun to the end of the storage ring. This configuration provided a range of testing environments in which to characterise the oBLM and investigate potential use cases. The results of these procedures demonstrated that the oBLM was able to objectively discern losses above 200 fC or approximately 10^6 electrons. The timing resolution as averaged from measurements using multiple fibres at several loss locations was determined to be 1.22 +/- 0.19 ns at FWHM across the working range of the fibres. When the oBLM is operated in time of flight mode this corresponds to a spatial resolution of 0.13 +/- 0.02 m, which is smaller than the average component spacing of lattice elements at the Australian Synchrotron and demonstrates that the oBLM is capable of attributing losses to specific errant devices. Potential and productive use cases of the oBLM were then explored and a range of operational techniques were developed, after which the oBLM was integrated into the injection efficiency monitoring and optimisation system. Where it was used, in time of flight mode, to characterise spontaneous losses along the length of the Australian Synchrotron injection and storage ring systems. The diagnostic information it provided from these measurements was employed in the tuning of the injection system and as a consequence the injection efficiency between the linac and booster ring was increased by 60 %. Based on the findings of this thesis an optimised configuration, that best enables the oBLM to address the usage scenarios identified, was created and presented in this thesis.

In modern-day technology, silicon and silicon-based materials play a key role in the production of computing parts, specifically, the transistors within the chips. The exponential densification of transistors has caused the excess heat generated during operation to significantly hamper chip performance. This has led to the rise of hyperbolic language which refers to this problem as the `silicon apocalypse', and the material as `dark silicon', on account of each chip mostly being turned off to limit heating. The focus of this work lies in creating a silicon-based heterostructure with diamond, which has an unparalleled thermal conductivity, to effectively extract and dissipate heat directly from the chip. To realise such a structure, this work explored the usage of single crystal diamond as a substrate for silicon growth. As diamond had been previously grown on silicon carbide with limited coherence, shown in literature by other authors, the work begins by investigating the interface between 3C-SiC and a diamond substrate both experimentally and theoretically. It was found that 3C-SiC could form a coherent interface with diamond across several nanometres and that, through atomistic simulation, it was possible to realise greater regions of coherence. In the fabrication process, which involved heating thermally deposited silicon within an ultra high vacuum chamber, it was discovered that thin film dewetting became a major hurdle for long range coherence. This dewetting phenomenon and the behaviour of silicon on diamond during annealing then became the second major focus of this thesis to better understand how, or if, a coherent interface could be achieved between these two materials. To diminish the possibility of dewetting, which occurs with very thin films, PECVD silicon was chosen as an accessible method to time-efficiently deposit thicker layers. In spite of the benefits of PECVD silicon, crystallisation through annealing did not yield single crystal silicon. Instead, minimal interaction was found below 600C between the diamond substrate and silicon, which exhibited behaviour in line with PECVD silicon on other substrates as reported in the literature. However, at elevated temperatures around 1000C, a novel form of diamond etching was observed. The results gleaned from this work indicated that 3C-SiC/diamond heterostructures with a coherent interface could be produced, and thus, future applications are possible. The formation of a silicon and diamond heterostructure, however, was hampered by thin film dewetting and so further testing is needed to determine whether a coherent interface could be achieved using processing techniques applied in the case of 3C-SiC, but with thicker layers. By utilising a more accessible deposition method, namely PECVD, thicker layers became readily available on diamond substrate. Under thermal treatment, the PECVD silicon was found to crystallise into a polycrystalline layer, and at temperatures exceeding 1000C, even begin etching the diamond substrate. These series of studies bring to light several fundamental details of a silicon and diamond interface that are a prerequisite to the utilisation of diamond substrates in the future, especially with silicon-based materials.

Quantum devices that leverage the manufacturing techniques of silicon-based classical computers make them strong candidates for future quantum computers. However, the demands on device quality are much more stringent given that quantum states can decohere via interactions with their environment. In this thesis, a detailed investigation of ion implantation induced defects generated during device fabrication in a regime relevant to quantum device fabrication is presented. We identify different types of defects in Si using various advanced electrical characterisation techniques. The first experimental technique, electrical conductance, was used for the investigation of the interface state density of both n- and p-type MOS capacitors after ion implantation of various species followed by a rapid thermal anneal. As precise atomic placement is critical for building Si based quantum computers, implantation through the oxide in fully fabricated devices is necessary for some applications. However, implanting through the oxide might affect the quality of the Si/SiO_2 interface which is in close proximity to the region in which manipulation of the qubits take place. Implanting ions in MOS capacitors through the oxide is a model for the damage that might be observed in other fabricated devices. It will be shown that the interface state density only changes significantly after a fuence of 10^13 ions/cm^2 except for Bi in p-type silicon, where significant increase in interface state density was observed after a fuence of 10^11 Bi/cm^2. The second experimental technique, deep level transient spectroscopy, was used to study the defects in the substrate of Si after ion implantation. As Er has the potential of interfacing electrical and optical properties of Si based quantum computers, it is important to know what defects will be present after the implantation because of its large atomic mass. H and Er implantation damages were compared to demonstrate the more complex defect evolution for Er implantation. Although defects were still present after a 400 C anneal, the concentration was reduced by at least one order of magnitude. The last experimental technique, charge pumping, was used on MOSFETs to study the interface state density directly in device structures that can be directly used in, for example, magnetic resonance and quantum sensing applications. Charge pumping has the potential of allowing measurement and manipulation of both electronic and magnetic properties of the interface defects and defects in the MOSFET channel. For such applications it may be necessary to operate the device close to absolute zero temperature. The work presented here represents a first step towards device and technique development with the ultimate aim of pushing measurements to mK temperatures where quantum device operations typically operate.

Establishing a baryogenesis mechanism, a dynamical origin of the baryon asymmetry, remains an open problem in physics. Electroweak baryogenesis is one such mechanism that is often touted for its inherent testability at current and near future experiments. Taking this notion to heart, here we will examine the collider and dark matter phenomenology of three models motivated by electroweak baryogenesis and novel electroweak phase transitions. In chapter 2, we extend the standard model with two real scalar singlets and one vector-like lepton doublet and examine the collider phenomenology, phase transition history, and baryogenesis mechanism. We find that such a model is capable of generating sufficient baryon asymmetry while satisfying electron electric dipole moment and collider phenomenology constraints. In chapter 3, we study the phenomenology of a hypercharge-zero SU(2) triplet scalar whose existence is motivated by two-step electroweak symmetry-breaking models. If the neutral component of the triplet is stable, we find that this model is strongly constrained by disappearing charged track searches and dark matter direct detection experiments. Conversely, if it is unstable, we find that this model is constrained by multilepton collider searches, such that a triplet with a mass less than 230 GeV is almost excluded at 95% confidence. In chapter 4, we examine the collider and dark matter phenomenology of the standard model extended by a hypercharge-zero SU(2) triplet scalar and a gauge singlet scalar. In particular, we study the scenario where both of the new scalars are charged under a single Z2 symmetry. We find that such an extension is capable of generating the observed dark matter density, while also modifying the collider phenomenology such that the lower bound on the mass of the triplet is smaller than in minimal triplet scalar extensions to the standard model.