Emergence is a philsophical concept that has proved to be attractive and long lasting. However in some forms, theories of emergence can be at odds with the process of deductive scientific research. Here I develop a theory of historical emergence based on our inability to describe, and therefore explain highly complex physical systems. To provide evidence for this hypothesis, I perform electronic struc- ture calculations on cyclobutadiene, iron arsenide, elemental iron, and manganese oxide using DFT. I find that only in the iron calculations was historical emergence found. I conclude that historical emergence is an effective definition of emergence, as only the iron calculations exhibited all the behaviour expected in a system that hosts emergence, namely dependent novelty, irreducibility, and unpredictability. Further, I propose a general theory that is able to calculate the wavefunction of the nuclei in an effective potential. I use this to calculate the Raman spectrum of cyclobutadiene, in which an energy splitting of vibrational energy levels is found due to tunnelling between two chemically equivalent rectangular configurations. I find that the structure of this spectrum, including the tunnelling splitting, can be explained by recourse to the typical motions predicted from a semiclassical model. I conclude that the properties different isomers cannot be calculated using a single generalised quantum calculation, even though isomers are composed of the same particles and have the same Hamiltonian. Therefore chemical systems are likely to host historically emergent explanations. From the analysis of single-crystal XRES measurements on FeAs, and symmetry considerations I propose a new canted magnetic structure commensurate with the incommensurate elliptical helical magnetic order. I justify this with an orbital projection method that is able to calculate the susceptibilities of the material to spin-orbit interactions. I also detail a spin initialisation procedure based on rotations of the exchange- correlation potential, that aims to reduce bias towards undesired density config- urations by the density search algorithms in noncollinear systems. I present its application to symmetry unconstrained, noncollinear calculations of manganese ox- ide and elemental iron. I conclude that this procedure is not suitable for systems with magnetic configurations robust to changes in their exchange and correlation potentials. Additionally symmetry unconstrained calculations are nontrivial, and future calculations will require modified density search algorithms to deal with sym- metry unconstrained calculations on many conductors due to complex interactions at the Fermi surface.

This thesis describes Rydberg spectroscopy and dressing experiments in an ultracold strontium gas. The strontium atoms are cooled to sub-uK temperatures in a narrowline magneto-optical trap, where Rydberg atoms are created using a two-photon excitation scheme. This required the development of a high-power ultraviolet laser system at 319 nm. The laser has a large tuning range for access to triplet Rydberg states from principal quantum numbers of 35 to > 300. By performing Rydberg spectroscopy in a magneto-optical trap, we show that narrow spectra can be obtained where the line centre is determined to ~ 10 kHz. A frequency comb is then employed to make absolute frequency measurements of optical transitions to accuracies of < 2 MHz. Techniques are outlined for improving the accuracy further, showing that overall uncertainties on the order of 10 kHz can be obtained. The reliable measurement of Rydberg levels is important for studying the variation in quantum defect across Rydberg series, and hence improving the accuracy of atomic models. In this work we also develop a novel system in which to realise Rydberg dressing. By resonantly coupling the excited state of the cooling transition to a high lying Rydberg state, we create a Rydberg-dressed magneto-optical trap. We demonstrate that the atoms acquire Rydberg properties, while undergoing continuous cooling at ~ 1 uK. The lifetime of the trap is proved to be sufficiently long to observe interactions, however the interaction strength is currently limited by the non-uniform spatial profile of the dressing beam. Straightforward methods to overcome this limitation are presented. As such this work should lead to future experiments, whereby tuneable long-range interactions can be observed in the dynamics of the dressed magneto-optical trap.

After 30 years since the first organic light emitting diode (OLED) was reported by Tang and VanSlyke, devices based on thermally activated delayed fluorescence (TADF) emitters have shown to be the most promising and efficient approach to convert dark triplet states into emissive singlet states. The TADF mechanism relies on thermal energy to raise the triplet state to a vibronic sub level that is isoenergetic with the singlet state, thus enabling reverse intersystem crossing (rISC) and allowing internal quantum efficiency values up to 100%. Major challenges faced by TADF studies persist, concerning the full understanding of the mechanism, as it is strongly affected by the environment in which the emitter is dispersed and the different conformations that the molecules can access. Throughout the course of this thesis, the photophysical and chemical properties of the TADF mechanism were investigated in various organic molecules including novel D-A-D and D-A3 molecules, bimolecular (exciplex) blends and excited state intramolecular proton transfer (ESIPT). Important new contributions towards the full elucidation of the TADF mechanism are presented, mainly regarding the current TADF vibronic coupling mechanism model, which highlights the need for three excited states (singlet charge transfer state; triplet charge transfer states; and triplet local excited state) to come into resonance to achieve high TADF efficiency. In addition, a solution to the dilemma that a TADF emitter cannot have both unity photoluminescence quantum yield and fast rISC rates is presented and high efficient OLEDs are shown. Moreover, it is discussed how different molecular conformers affect the efficiency of the TADF mechanism by studying molecules that show dual charge transfer emission. Furthermore, it is shown that the emitter and host combination must be optimized to minimize the rISC barrier and maximize the TADF in blue OLEDs. Additionally, the use of ESIPT emitters to generate TADF is discussed.

The upcoming Dark Energy Spectroscopic Instrument (DESI) and Euclid galaxy surveys aim to make the most precise galaxy clustering measurements yet in order to probe the nature of the mysterious dark energy that is thought to make up the majority of the energy density of the Universe today. To reach the required precision, it is essential that the systematics that affect these measurements are understood, which requires realistic mock galaxy catalogues. This thesis focuses on building a mock catalogue for the DESI Bright Galaxy Survey (BGS), and applications of this mock. We outline the methods used to create halo merger trees from N-body and Monte Carlo simulations, which is the first step towards creating a mock catalogue. We show how these methods can be extended beyond ΛCDM to warm dark matter, and show applications. We have developed a halo occupation distribution (HOD) method for creating a BGS mock catalogue from the Millennium-XXL (MXXL) simulation, with galaxies being assigned r-band magnitudes and g-r colours. The mock catalogue is able to reproduce the luminosity function and clustering of the Sloan Digital Sky Survey (SDSS) and Galaxy And Mass Assembly (GAMA) survey at different redshifts. The mock is used to quantify incompleteness in the DESI BGS due to fibre assignment, which depends on the surface density of galaxies, and to assess correlation function correction methods. An inverse pair weighting method is able to provide an unbiased correction on all scales. Finally, we show how the HOD methodology can be extended to construct mock catalogues for Euclid, and other large galaxy surveys.

The Standard Model of particle physics does not provide a complete description of nature, there are many questions that remain unsolved. In this work, we study the theory and phenomenology of different models beyond the Standard Model that address some of its shortcomings. Motivated by naturalness arguments, we discuss the idea of classical scale invariance where all the fundamental scales are generated dynamically via quantum effects. We apply this approach to an extension of the inert doublet model and present a model that addresses the dark matter, neutrino masses and the baryon asymmetry of the Universe simultaneously. We then study a set of simplified models of dark matter to address the effects of three-point interactions between the dark matter particle, its dark coannihilation partner, and the Standard Model degree of freedom, which we take to be the tau lepton. In these models, the contributions from dark matter coannihilation channels are highly relevant for a determination of the correct relic abundance. Firstly, we investigate these effects as well as the discovery potential for dark matter coannihilation partners at the LHC by searches for long-lived electrically charged particles. Secondly, we study the sensitivity that future linear electron-positron colliders will have to these models for the region in the parameter space where the coannihilation partner decays promptly. Lastly, we discuss an observable for the detection of ultralight axions. In the presence of an ultralight axion, a cloud of these particles will form surrounding a rotating black hole through the mechanism of superradiance. This inhomogeneous pseudo-scalar field configuration behaves like an optically active medium. Consequently, as light passes through the axion cloud it experiences polarisation-dependent bending, we argue that for some regions in the parameter space of axion-like particles this effect can be observed by current radio telescope arrays.

This thesis focuses on modeling and measuring pairwise statistics in large galaxy redshift surveys. The first part focuses on two point correlation function measurements relevant to the Euclid and DESI BGS surveys. Two point measurements in these surveys will have small statistical errors, so understanding and correcting for systematic bias is particularly important. We use point processes to build catalogues with analytically known two point, and for the first time, 3-point correlation functions for use in validating the Euclid clustering pipeline. We build and summarise a two point correlation function code, \texttt{2PCF}, and show it successfully recovers the two point correlation function of a DESI BGS mock catalogue. The second part of this thesis focuses on work related to the PAU Survey (PAUS), a unique narrow band wide field imaging survey. We present a mock catalogue for PAUS based on a physical model of galaxy formation implemented in an N-body simulation, and use it to quantify the competitiveness of the narrow band imaging for measuring novel spectral features and galaxy clustering. The mock catalogue agrees well with observed number counts and redshift distributions. We show that galaxy clustering is recovered within statistical errors on two-halo scales but care must be taken on one halo scales as sample mixing can bias the result. We present a new method of detecting galaxy groups, Markov clustering (MCL), that detects groups using pairwise connections. We explain that the widely used friends-of-friends (FOF) algorithm is a subset of MCL. We show that in real space MCL produces a group catalogue with higher purity and completeness, and a more accurate cumulative multiplicity function, than the comparable FOF catalogue. MCL allows for probabilistic connections between galaxies, so is a promising approach for catalogues with mixed redshift precision such as PAUS, or future surveys such as 4MOST-WAVES.

In this thesis I describe the development, implementation and characterisation of a source of wavelength-tunable few-femtosecond laser pulses in the deep ultraviolet spectral region for use in time-resolved experiments. I also propose and model an extension of this source capable of simultaneously generating a single-cycle driving pulse for extreme nonlinear optics as well as a few-femtosecond ultraviolet pulse. Building on advances in the field of femtochemistry, ultrafast science is moving towards ever shorter timescales and more complex systems. One of the key building blocks for the next generation of experiments studying ultrafast dynamics in molecules will be the availability of few-femtosecond pulses to directly address electronic resonances whose corresponding photon energy lies in the vacuum and deep ultraviolet spectral regions. By harnessing the capabilities of soliton self-compression in novel micro-structured waveguides, we have generated pulses in the deep ultraviolet with energies of hundreds of nanojoules. The delivery of these pulses to an experiment as well as the measurement of their temporal profile pose significant challenges due to the dispersive properties of optical materials in the ultraviolet. We have developed an in-vacuum device for ultrafast pulse characterisation, and by directly coupling the waveguide to vacuum we were able to measure distortion-free pulses with durations below 10 fs at a range of different central wavelengths. Numerical modelling of a scaled-up version of the apparatus shows that the self-compressed driving pulse in the ultraviolet pulse generation process can maintain its shape when delivered directly to vacuum. The single-cycle pulse duration makes it an ideal driver for extreme nonlinear optics and the generation of isolated attosecond pulses in the soft X-ray spectral region.

Topical pharmaceuticals are a vitally important part of modern medicine. Currently, characterising the dermatopharmacokinetics of these drugs is very difficult, and not possible in either real-time, or with a high level of accuracy. This thesis applies three coherent Raman scattering microscopy techniques to the challenge of video-rate monitoring of a porcine skin model undergoing penetration by two different, widely used, pharmaceuticals. It was found that the data taken during these time-course experiments could be used in conjunction with a Beer-Lambert expression, and Fick’s second law, to extract valuable permeation data – namely the skin-solute partition coefficient, and diffusion coefficient – of these pharmaceuticals.

This thesis presents the development of a toolbox for the coherent control of ultracold polar molecules. Such systems of molecules promise the creation of long-lived, highly dipolar quantum gases with applications spanning the fields of quantum state controlled chemistry, quantum information, quantum simulation, and precision measurement. However, the addition of vibrational and rotational degrees of freedom leads to molecular systems being significantly more complex than their widely used atomic counterparts. In this work we demonstrate full control of the quantum state down to the hyperfine level of an optically trapped sample of ultracold bosonic 87Rb133 Cs molecules, and exploit that control to begin an investigation into the collision processes which take place in an ultracold molecular gas. We create a sample of up to ∼ 4000 optically trapped molecules in their rovibronic and hyperfine ground state. We characterise the molecules by measuring their temperature, binding energy, and molecule-frame electric dipole moment. We perform spectroscopy of the first rotationally excited state with hyperfine state resolution using microwaves to determine accurate values of rotational and hyperfine coupling constants. We use coherent π pulses to perform complete transfer population between selected hyperfine levels of the ground, first-excited, and second-excited rotational states. We investigate the effect of the off-resonant light of our optical dipole trap on the rotational and hyperfine structure of the molecules. Through a combination of high-resolution microwave spectroscopy and parametric heating measurements, we characterise the polarisability of the 87Rb133Cs molecule. We demonstrate that coupling between neighbouring hyperfine states manifests in rich structure with many avoided crossings in any rotational state other than the ground state. This coupling may be tuned by rotating the polarisation of the linearly polarised trapping light. Finally, we study the lifetime of polar bosonic 87Rb133Cs molecules in our 3D optical dipole trap. We examine the lifetime of the molecules as a function of dipole trap intensity, magnetic field, and hyperfine and rotational state. Despite the chemical stability of the 87Rb133 Cs molecule, we observe lifetimes of ∼1 s corresponding to 2-body decay rates close to the universal limit.

The design of a modular moving trap Zeeman decelerator capable of decelerating gas pulses produced from a supersonic source is presented here. Unlike the conventional form of Zeeman decelerator, paramagnetic particles are confined in a 3D potential throughout the deceleration process. The decelerator field is produced by flattened helical coils and currents of up to 1000 A peak. As the coils are periodic in nature, each coil produces a number of deep, quadrupole traps along the molecular beam axis. The resultant periodic field is described as a travelling wave. The application of the appropriate time dependent current allows the traps to move through the four coil modules. In order to compensate for the weaker transverse confinement, a quadrupole guide, operating at 700 A DC, is required to prevent further losses during the deceleration process. The operation of the decelerator relies on the power electronics developed specifically for the quadrupole and the decelerator coils. Due to the electromagnetic interference generated through the switching of the large currents, much of the electronics used to control the power electronics had to be developed specifically. The quadrupole power electronics have been designed to produce fast switching edges. This is necessary to minimise the interaction of the particles within the fringe field regions while maximising the interaction time within the pure quadrupole field. Even at a modest voltage applied to the circuitry, the rise time in current to 700 A has been reduced by a half. The decelerator power electronics must be capable of producing an alternating waveform with an amplitude of at least 500 A for each of the coil phases. Furthermore, the frequency of the waveforms must be tunable within a range of 10 kHz to 0 Hz. Through a combination of pulse width modulation and knowledge of the electrical properties of the coil it is possible to synthesise an alternating current waveform from a 800 V DC supply using a suitable switching circuit. %The challenge of switching such high powers is the transient voltage spikes that can be produced, however, these can be avoided through careful consideration of the layout of the circuit. Decelerators such as this do not cool the sample but instead reduces the mean velocity of a subset of particles which remained trapped. This maintains the phase space density of trapped particles. Modelling the magnetic fields generated by the decelerator coils has been necessary in order to understand the phase space acceptance of the decelerator. The helical nature of the coils required the development of a specific algorithm in order to calculate the field generated by each wire element. The resultant potential can then be interpolated using a tricubic interpolator to extract the field gradients necessary for numerical simulations of the particle trajectories. Including the effects of the pulse width modulated on the trap facilitates the characterisation of the acceptance of the decelerator and the limitations of the current iteration of the design. The numerical simulations can also be compared to experimental results gathered for metastable argon. The 3D guiding, or velocity bunching, of the gas packet over a range of velocities has been demonstrated. The ability to 3D guide and decelerate were severely hampered by the failure of key electronic components, limiting three coils to 100 A peak, moreover, these traps were sub-optimally loaded. Deceleration from 350 to 347 m/s and 342 to 310 m/s has been observed. The design of a trap capable of simultaneously loading samples of decelerated CaH and Li while allowing the cooling of Li would potentially allow for the sympathetic cooling of a molecular species with an atomic refrigerant. This particular atom-molecule system would also facilitate the examination of controlled chemistry and collisions over a range of temperatures through state selection of the reactants. The loading of the trap has been optimised in 1D for CaH with a loading efficiency of 52.2 % while only 7.3 % of Li is loaded when each of the gas packets has a mean velocity of 11 m/s. This implies that the source of the Li must be at least 130 times brighter than that of the CaH.