Bose–Einstein condensates with attractive interactions have stable 1D solutions in the form of bright solitary-waves. These solitary waves behave, in the absence of external potentials, like macroscopic quantum particles. This opens up a wide array of applications for the testing of quantum mechanical behaviours and precision measurement. Here we investigate these applications with particular focus on the interactions of bright solitary-waves with narrow potential barriers. We first study bright solitons in the Gross–Pitaevskii equation as they are split on Gaussian and δ-function barriers, and then on Gaussian barriers in a low energy system. We present analytic and numerical results determining the general region in which a soliton may not be split on a finite width potential barrier. Furthermore, we test the sensitivity of the system to quantum fluctuations. We then study fast-moving bright solitons colliding at a narrow Gaussian potential barrier. In the limiting case of a δ-function barrier, we show analytically that the relative norms of the outgoing waves depends sinusoidally on the relative phase of the incoming waves, and determine whether the outgoing waves are bright solitons. We use numerical simulations to show that outside the high velocity limit nonlinear effects introduce a skew to the phase-dependence. Finally, we use these results to analyse the process of soliton interferometry. We develop analyses of both toroidal and harmonic trapping geometries for Mach–Zehnder interferometry, and then two implementations of a toroidal Sagnac inter- ferometer, also giving the analytical determination of the Sagnac phase in such systems. These results are again verified numerically. In the Mach–Zehnder case, we again probe the systems sensitivity to quantum fluctuations.

This thesis describes the design and construction of a new apparatus to laser cool and trap Yb and Cs atoms with the ultimate aim of creating ultracold molecules with both an electric and magnetic dipole moment, which are of great interest in a range of fields. The Yb and Cs atomic beams are first generated and overlapped in a dual species oven. A collimated atomic beam of the two species is formed by the use of an array of capillary tubes at the exit of the oven. At this stage the atoms have an average velocity of 311m/s or 264m/s for Yb and Cs respectively, therefore it is necessary to reduce their velocity before they can be trapped in a magneto-optical trap (MOT). This initial stage of slowing is carried out with a Zeeman slower. Due to their atomic properties, Yb and Cs atoms are unable to be slowed by the same magnetic field profile therefore they cannot be loaded simultaneously, however, the Zeeman slower can load the atoms into a MOT sequentially. Once their velocities have been reduced to approximately 48m/s (10m/s) the Cs (Yb) atoms can be captured in a MOT. The laser systems for cooling Yb and Cs are also presented. Laser cooling of Cs is achieved on the D2 transition at 852.3nm whereas Yb can either be cooled on the 1S0 to 1P1 or 1S0 to 3P1 transitions at 398.9nm or 555.8nm respectively. Due to the relative linewidths of these transitions (2π×28.0MHz and 2π × 182.2kHz), Zeeman slowing is performed for Yb on the 1S0 to 1P1 transition and magneto-optical trapping on the 1S0 to 3P1 transition. A Cs MOT with 1 × 10^8 atoms and an Yb MOT with the order of 10^8 atoms on the narrow 556nm transition are demonstrated. The mixture can be sequentially loaded into a dual species MOT, paving the way for many further experiments exploring this novel mixture.

This thesis details the first measurements of Rydberg dipole blockade in a cold ensemble of divalent atoms. Strontium atoms are cooled and trapped in a magneto-optical trap and coherently excited to Rydberg states in a two-photon, three-level ladder scheme. Owing to the divalent nature of strontium, one electron can be excited to the Rydberg state, whilst the other lower-lying electron is available to undergo resonant optical excitation to autoionising states, which ionise in sub-nanosecond timescales. The remaining ions that are recorded on a micro-channel plate are proportional to the number of Rydberg atoms. The development of a narrow linewidth laser system necessary for an additional stage of cooling is explained and characterised. Two frequency stabilisation schemes are discussed: one to address the short-term laser frequency instabilities based on the Pound-Drever-Hall technique; the other to address the long-term laser frequency instabilities based on Lamb-dip spectroscopy in an atomic beam. The cooling dynamics on the narrow cooling transition is studied experimentally and modelled via theoretical simulations.

At the centre of every massive galaxy there resides a super-massive black hole that grew during periods of active galactic nuclei (AGN) activity. Current theoretical models of galaxy evolution invoke AGN-driven galaxy-scale feedback processes (e.g., the expulsion of gas through outflows) in order to reproduce many of the fundamental properties of galaxies and the intergalactic medium. This thesis uses observations to test some of the predictions of these feedback processes. I present integral field unit observations of AGN host galaxies to trace their ionised gas kinematics. The targets are eight high-redshift (z=1.4-3.4) ultra-luminous infrared galaxies, that are representative of rapidly evolving distant galaxies, and sixteen z<0.2 luminous AGN, that were selected from a parent sample of ~24,000 sources to be representative of the overall population. In both samples I identify galaxy-wide outflows (i.e., over kiloparsec scales), calculate their properties (e.g., mass outflow rates and energetics) and show that they are broadly consistent with theoretical predictions. I find that ionised outflows are common in z<0.2 luminous AGN and are consistently extended over kiloparsec scales (in >70% of cases). I also use far-infrared Herschel data of X-ray detected z=1-3 AGN to test the prediction that luminous AGN shut down star formation in their host galaxies. Using stacking techniques I show that, on average, X-ray detected AGN over a wide range of luminosities (i.e., L(2-8keV)~10^42-10^45) erg/s) have star formation rates that are consistent with non-active galaxies. This may imply that luminous AGN do not impact upon the star formation in their host galaxies. Overall, this thesis demonstrates that energetic galaxy-wide outflows are prevalent in AGN host galaxies; however, it also demonstrates that we still lack direct observational evidence that luminous AGN are suppressing star formation in their host galaxies.

Printed electronics is an established industry allowing the production of electronic components such as resistors, and more complex structures such as solar cells, from functional inks. Composites, a mixture of two or more materials with different physical and/or chemical properties that combine to create a new material with properties differing from its constituent parts, have been important in areas such as the textile and automotive industries, and are significant in printed electronics as inks for printed circuit components, touch and vapour sensors. Here, the functional performance and physical behaviour of two screen printable multi-component nanocomposite inks, formulated for touch-pressure sensing applications, are investigated. They each comprise a proprietary mixture of electrically conducting and insulating nanoparticles dispersed in an insulating polymer binder, where one is opaque and the other transparent. The opaque ink has a complex surface structure consisting of a homogeneous dispersion of nanoparticles. The transparent inks structure is characterised by large aggregates of nanoparticles distributed through the printed layer. Temperature dependent electrical transport measurements under a range of compressive loadings reveal similar non-linear behaviour in both inks, with some hysteresis observed, and this behaviour is linked to the inks structures. A physical model comprising a combination of linear and non-linear conduction contributions, with the linear term attributed to direct connections between conductive particles and the non-linear term attributed to field-assisted quantum tunnelling, has been developed and used successfully to describe the underpinning physical processes behind the unique electrical functionality of the opaque ink and, to a lesser extent, the transparent ink.

We investigate the growth of black holes and their effects on the evolution of galaxies through cosmic time in the ΛCDM cosmology by using fully hydrodynamical simulations of structure formation. Gas accretion onto black holes is modelled and improved via a subgrid model that takes into account the circularisation and subsequent viscous transport of infalling material. We incorporate the black hole accretion model in hydrodynamical simulations of relatively small size. The model broadly matches the observed stellar mass fractions in haloes and reproduces the expected correlation between the stellar velocity dispersion and the black hole mass. The distribution of black hole accretion rates is also compatible with observations. Additionally, we use a state-of-the-art hydrodynamic simulation that is designed to produce a virtual Universe that closely matches the observed properties of galaxies such as the galaxy stellar mass function and the relation between the black hole mass and the stellar mass at the present day. The critical part to reproduce the galaxy stellar mass function is the subgrid models of AGN feedback and black hole growth that are based on the model investigated above. We find that the simulation reproduces the black hole mass function at the present day. We investigate the predicted relations between the black hole mass and the stellar mass and the black hole mass and the parent halo mass and their evolution through cosmic time. We find that there is no evolution in approximately the last 10 and a half Giga years (z < 2), while at early times the most massive galaxies were inhabited by more massive black holes. The evolution of these relations are different in large halos and small halos. This can be explained in terms of self-regulation. Black holes living in massive haloes (< 10^12 M ) today self-regulate their growth via AGN feedback that quenches black hole accretion rates and star formation, while the black holes in small haloes rapidly grow without affecting the growth of the galaxy. By looking at the relations between the gas properties and the parent halo mass, we compare the scatter of these relations to the ratio of cumulative accreted mass of black holes to halo mass. We speculate that there is a range of halos that frames the region where black holes start to grow by self-regulation. Finally, we explore the predicted evolution of the AGN luminosity functions in X-ray bands predicted in this simulation. We find remarkable agreement with observations. In addition, we find that the observed downsizing effect of AGNs is well reproduced in the simulation as a natural consequence of reproducing the AGN luminosity functions. We also explore AGN activity in different halos. We find that the massive haloes are inhabited by AGNs with low or non activity while low mass haloes are inhabited by AGNs with high activity that contribute to the hard X ray luminosity function across time.

Over the last ~20 years, the importance of dusty star-forming galaxies in contributing approximately half the energy density of the Universe has been realised. Much research in this field has focused on the subset of submillimetre bright galaxies (SMGs). Submillimetre Astronomy has recently seen major advances due largely to huge developments in the available instrumentation. In this thesis I present the first spectroscopic redshift distribution of unambiguously-identified SMGs, targeted with ALMA. The redshift distribution is shown to peak at z~2.4. The next step to understanding the SMG population is to use their redshifts to facilitate high-resolution follow-up observations, probing the conditions and physical structure within the interstellar medium (ISM) of these systems. I present the detailed observations of the ISM within the gravitationally lensed SMG, SMMJ2135. In particular, the spectral line energy distributions of 12CO, 13CO and C18O are measured and used to infer the temperature, densities and chemical abundances within this intrinsically representative SMG, with strong variation found between the multiple kinematic components in the galaxy. Furthermore, an unusually high abundance of C18O is measured, implying the presence of preferentially massive stars, perhaps highlighting some differences between star formation locally and at high-redshift. The cosmic star-formation rate density has rapidly declined since z~2 and there is much evidence to suggest that massive star-forming galaxies at z~2 may evolve into massive passive elliptical galaxies at z=0. I investigate the potential influence of active galactic nuclei (AGN) on the suppression of star formation within massive elliptical galaxies over z=0.1-1.2. I determine that the hot gas within these evolved systems does not cool as rapidly as expected and demonstrate that heating due to mechanical feedback from radio AGN is more than sufficient to balance the X-ray cooling of hot gas, thus suppressing further star formation.

The methods by which modern event generators incorporate matrix elements accurate to next-to-leading order in the strong coupling for inclusive observables, as well as how such amplitudes are combined with the parton shower algorithms are overviewed and a novel implementation of both to Beyond-the-Standard-Model constructions for processes with non-coloured final states is presented. This implementation is applied to Z' models inspired on E_6 grand unified theories as well as to supersymmetric scenarios involving pair production of the supersymmetric partners to the Standard Model leptons and gauge bosons/Higgs. Total cross sections are verified to be in agreement with results from pre-existing software packages and observables inclusive in jets are presented at novel NLO accuracy with local increases in cross section properly accounted for and scale variation reduced. The modest increases in cross section and reduction in theoretical uncertainty make the use of the present implementation for searches at the Large Hadron Collider highly desirable.

This thesis proposes a novel method to implement universal quantum gates for photonic qubits using the strong dipole-dipole interactions present in a cold gas of Rydberg atoms and the control offered by microwave fields. By means of electromagnetically induced transparency (EIT) we store the information encoded in photonic qubits as Rydberg excitations, and then couple these to neighbouring states using microwaves. Microwaves alter the range of the dipole-dipole interactions between the excitations, and a suitable geometrical arrangement of the excitations in the cloud leads to a controlled π phase shift in the system's wavefunction, the basis of the universal gates proposed. After processing, the excitations in the medium are later retrieved as photons. A theoretical description of the implementation of a 2-qubit universal gate is presented and a numerical analysis shows the feasibility of its implementation in a cold cloud of Rubidium atoms. A scheme is also proposed to construct more general gates with applications in quantum information processing. These schemes have been made possible by the analysis of recent experiments performed in the group. This analysis is repeated here, along with the characterization of parts of the detection system required to obtain them.

DFT is a method that deals eciently with the ground state any-electron problem. It replaces the solution of the many-electron Schrodinger's equation with an equation to determine the electronic density alone. In the Kohn-Sham (KS) scheme, this density is obtained as the ground state density of a ctitious system of non-interacting electrons. The aim is to determine the local potential for these electrons so that their density equals the interacting density of the physical system. This potential is the sum of the electron-nuclear attraction, the Hartree repulsion from the density and nally the exchange and correlation potential. The central approximation in DFT is the functional form of the exchange-correlation potential. The most basic approximate functionals are explicit functions of the electron density. More sophisticated approximations are orbital dependent functionals or hybrids of density and orbital dependent functionals. In this work we present the implementation of some accurate local exchange potentials, the exact exchange (EXX) potential, the local Fock exchange (LFX) potential and an approximation to EXX, the common energy denominator approximation (CEDA) potential. The EXX potential minimises the Hartree-Fock (HF) total energy and is calculated using perturbation theory and the Hylleraas variational method, improving upon previous implementations. Optimising a local potential that adopts the HF density as its own ground state density, gives the LFX potential, which is simple to calculate and physically equivalent to the EXX potential. Both the EXX and LFX methods are extended to be applicable to metallic systems. The implemented potentials are used to calculate the electronic band structures for semiconductors, insulators, antiferromagnetic insulators and metals. For the semiconducting, insulating and metallic systems studied, the LFX method gives very similar results to EXX. In the systems characterised by stronger correlations, we observe a small disparity between the two exchange methods. When compared to experiment, the results are surprisingly accurate, given the complete neglect of correlation in these calculations. This is remarkable for the strongly correlated systems and also for the simple metals, given the well-known qualitative failure of Hartree-Fock for metals. The fundamental gap of a system is the sum of the KS eigenvalue gap and a correction known as the derivative discontinuity. The exact derivative discontinuity for a system is derived from ensemble density functional theory, thus allowing the full calculation of fundamental band gaps. Approximate forms of the discontinuity for the local density approximation (LDA), generalised gradient approximations (GGA), EXX and LFX are also derived and implemented. Contrary to the accepted wisdom, that the derivative discontinuity for local approximations (LDA/GGA) vanishes, calculated LDA and GGA fundamental band gaps give a much improved result over the corresponding Kohn-Sham band gaps, with accuracy comparable to EXX and LFX KS band gaps. Finally the derivative discontinuity using exact exchange and an orbital dependent correlation functional was also derived but not implemented.