This thesis describes theoretical and experimental work concerning radiation forces on atoms, with particular reference to rubidium atoms confined in a magneto-optical trap. After a short history of the field of laser cooling, a review of the semiclassical theory of mechanical interactions between two-level atoms and electromagnetic radiation is given. Different formulations of the semiclassical theory are discussed, including a new formulation in terms of momentum transfer amongst the plane wave modes of the electromagnetic field. Two important applications of light forces on atoms, namely 'optical molasses' and the 'magneto-optical trap', are then described with emphasis on experimental parameters. Three sub-Doppler cooling mechanisms, 'sisyphus cooling', 'motion-induced orientation cooling' and the 'magnetically-assisted sisyphus effect', are described and their role in optical molasses and the magneto-optical trap is discussed. A new study of the polarisation gradients which occur in 3-D monochromatic light fields is presented and quantifies their relative presence in different light field configurations. Polarisation gradient parameters are developed and shown to be directly related to the relativistic spin tensor of the light field. Implications of this polarisation gradient study for laser cooling work are discussed. The design, construction from scratch, operation and testing of a magneto-optical trap for rubidium are described, including novel designs for two vacuum cells. Preliminary experiments to characterise the trap are described and results are presented; they primarily concern the number and distribution of atoms in the trap. Finally. the theory of time domain spectroscopy is reviewed. The construction and testing of a pulsed dye laser for study of coherent transients in samples of laser-cooled atoms and a proposed experiment to measure the temperature of cold atoms using coherent transients are described. Factors expected to influence the shape of coherent transients in cold atoms are discussed.

No description available.

Diamond is a radiation-hard material with a wide band-gap which is typically electrically insulating. A wide range of diamond-based material is available, including natural gemstones and synthetic diamondmanufactured by chemical vapour deposition (CVD) and high pressure and temperature (HPHT) techniques. The wide band-gap and electrical insulation properties mean that defects introduced by irradiation and plastic deformation, during growth or otherwise, may exist in more than one charge and/or electronic-spin state. Of these, defects with unpaired electrons give rise to characteristic spectroscopic signatures in electron paramagnetic resonance (EPR) experiments. In favourable situations these spectra provide chemical specificity, defect symmetry, effective spin-state, and wave function character (such as sp hybridisation), and when combined with temperature effects can yield data relating to thermal stability (for example binding and migration energies) and temperature dependent symmetry effects. Recent advances in quantum chemical simulation allow for reasonable accuracy in simulated hyperfine interaction (HFI) tensors (electron-spin and nuclear-spin interactions). Indeed, many assignments for EPR centres are tentative in nature. Where the proposed model yields calculated hyperfine values that differ substantially from those measured, in addition to refuting the current model, an examination of a wide range of candidate defects may lead to more realistic models. Defects observed in natural and synthetic diamonds provide a finger-print of their differing growth conditions, as well as the thermal and mechanical processes they have experienced. A challenge that has existed for decades in the effort to produce diamond suitable for electronics is in overcoming the difficulty in production of low resistivity n-type material. N, a dopant one might naively assume would be effective, undergoes a significant structural relaxation, rendering it a very deep donor at around Ec − 1.7 eV. Phosphorus is a better candidate since the substantial difference in atomic radius relative to the host suppresses large structural relaxations associated with nitrogen. However, with a donor level at around 0.6 eV below the conduction band, it has a low ionisation fraction at room temperature. This thesis presents the results of calculations performed with the ab initio modelling (AIMPRO) code. The initial stages studied the stability, defect symmetry, Kohn Sham orbitals and the hyperfine interaction of di-nitrogen substitutionals diamond. Analysis was then conducted of nitrogen pair defects relating to published theoretical and experimental models of W24, N1, W7, M2, N4 and M3 electron-paramagnetic-resonance centres in diamond in which pairs of nitrogen donors are separated by different numbers of intervening host sites, both in ionised S = 1/2 and neutral S = 1 forms. Using density functional techniques, these models are confirmed, but in order to do so for the N4 centre, for example, it is shown to be essential that extremely low energy reorientation takes place. Charge exchange and chemical re-bonding effects also provide an explanation for the distinct forms of the S = 1 neutral configurations observed. Other proposed models were then considered, including a detailed analysis of the hyperfine interactions formuoniumcentres, including the effects of vibration. This was combined with the experimental examination of N-containing diamond, where muon-spin relaxation experiments suggest a strong interaction between N-aggregates and the implanted muon. Structures made from two arrangements of pairs of substitutional nitrogen and oxygen showed no direct evidence for the involvement of the oxygen. The proposed model for N3 broadly agreed with experimental results but not for the OK1 centre. Despite its high ionisation energy, the n-type dopant of choice in diamond is currently phosphorus. Chemical vapour deposited diamond can be grown with high concentrations of P, and the substitutional donor has been characterised via a number of experimental techniques including electron paramagnetic resonance. Substitutional P undergoes a Jahn-Teller distortion at low temperature, where the EPR tensors reflect a tetragonal symmetry. Other P-containing EPR centres have also been detected but their structure remains uncertain.

We compute the quark and gluon form factors at up to three-loop order within massless perturbative Quantum Chromodynamics by studying the photon-quark-anti-quark vertex and the effective vertex of a Higgs boson and two gluons. We use Feynman diagram methods to derive expressions for the form-factors in terms of tensor loop integrals in $D=4-2\epsilon$ dimensions. We review various methods for relating tensor integrals to a basis set of master integrals and utilize the FIRE package based on Integration-By-Parts to perform the reduction, thereby enabling the form factors to be expressed (in $D$-dimensions) as a sum of master integrals. We assemble the known results for master integrals and use them to provide a Laurent expansion in $\epsilon$ through to $\mathcal{ O}(\epsilon^{0})$. The results for the three-loop form factors may provide the building blocks for many third-order cross section calculations.

In this thesis, the dynamics of cold, trapped atomic gases are investigated, and the prospects for exploiting their nonlinear dynamics for inertial sensing are discussed. In the first part, the resonant and antiresonant dynamics of the atom-optical quantum delta-kicked accelerator with an initial symmetric momentum distribution are considered. The system is modelled as an ideal, non-interacting atomic gas, with a temperature-dependence governed by the width of the initial momentum distribution. The existence of resonant and antiresonant behaviour is established, and analytic expressions describing the dynamics of momentum moments of the time-evolved momentum distribution are derived. In particular, the momentum moment dynamics in both the resonant and antiresonant regimes depend strongly on the width of the initial momentum distribution. The resonant dynamics of all even-ordered momentum moments are shown to exhibit a power-law growth with an exponent given by the order of the moment in the zero-temperature regime, whereas for a broad, thermal initial momentum distribution the exponent is reduced by one. The cross-over in the intermediate regime is also examined, and a characteristic time is determined up to which the system exhibits dynamics associated with the zero-temperature regime. A similar analysis is made for the temperature-dependence of the antiresonant dynamics. This general behaviour is demonstrated explicitly by considering a Maxwell-Boltzmann and uniform momentum distribution, allowing exact expressions describing the dynamics of the second- and fourth-order momentum moments, and momentum cumulants, to be obtained. The relevance of these results to the potential of using this system in accurate determinations of the local gravitational acceleration is discussed. In the second part, the dynamics of one- and two-component Bose-Einstein Condensates prepared in a counter-rotating superposition of flows in a quasi-1D toroidal trap are studied. Particular attention is paid to the dynamical stability of the initial state in the presence of atom-atom interactions, included via a mean-field description within the Gross-Pitaevskii equation. A broad regime of dynamical stability using a two-component BEC is identified, in which a typical implementation using Rb-87 is predicted to lie. A proof-of-principle Sagnac atom-interferometer using a two-component Rb-87 BEC is then presented, and the accumulation of the Sagnac phase is shown to be possible via relative population measurement or, alternatively, through the continuous monitoring the precession of atomic density fringes. In contrast to conventional Sagnac interferometers, the accumulation of the Sagnac phase is independent of the enclosed area of the interferometer. The prospects of using this system for high-precision determinations of rotation is discussed.

The sensitivity of s and p wave positron-hydrogen atom elastic-phase shifts, to the presence or absence of various multipole components of the adiabatic polarisation potential is discussed. It is concluded that higher multipoles than the quadrupole component are unimportant and support is given to the view of Drachman (1965) that in s-wave scattering the monopole component of the adiabatic potential should be suppressed. Then the cross-section for positronium formation by positron impact on hydrogen is calculated in the two-state approximation, taking account of the polarisation of the hydrogen and positronium atoms in each channel. It is found that the polarisation forces dominate the cross-section near the threshold for positronium formation and evidence is presented for the existence of a positronium-proton bound state that gives rise to a resonance in elastic e(^+) –H scattering just below the formation threshold.

In this thesis we describe a procedure for isolating the infrared singularities present in gluonic scattering amplitudes at next-to-leading and next-to-next-to-leading order. We adopted the antenna subtraction framework which has been successfully applied to the calculation of NNLO corrections to the 3-jet cross section and related event shape distributions in electron-positron annihilation. We consider processes with coloured particles in the initial state, and in particular two-jet production in hadron-hadron collisions at accelerators such as the Large Hadron Collider (LHC). We derive explicit formulae for subtracting the single and double unresolved contributions from the double radiation gluonic processes using antenna functions with initial state partons. We show numerically that the subtraction term effectively approximates the matrix element in the various single and double unresolved configurations.

The primary goal of the future experimental program in neutrino oscillation physics is to determine the size of the unknown mixing angle, θ₁₃, whether CP-violation is present in the leptonic sector and the sign of the atmospheric mass squared splitting. If θ₁₃ is not found by upcoming experiments, then we must turn to intense sources of neutrinos: the Superbeam, Neutrino Factory or Beta Beams. The phenomenon and present status of neutrino oscillations is introduced and future experimental options and some of the strategies summarised. A measurement of θ₁₃ and the CP-phase δ requires a search of sub-dominant appearance events, such as Ve → Vμ. In general, neutrino appearance data can accommodate up to 8 different solutions. This 'problem of degeneracies' is discussed and some of the strategies to resolve them are highlighted. A Beta Beam is an intense, clean and collimated electron neutrino beam sourced from the the acceleration of radioactive ions. In this thesis, the ability of Beta Beams, using a neutrino run only, to resolve these degeneracies is explored. The energy dependence of the neutrino oscillation probability and degeneracies is exploited to achieve a good overall CP-violation reach. This approach is adapted to the variants on the Beta Beam idea; namely the electron capture beams and hybrid beams. It is found for all cases considered that the reach is heavily dependent on the event rate with degeneracies causing major problems for low luminosity machines. The need for high event rates suggests that electron capture and hybrid machines will not be competitive without extensive R&D. The single ion Beta Beam is a viable alternative to the dual ion Beta Beams considered in the literature. Future studies may indicate that it in fact has a better overall physics reach.

In this thesis we investigate the static properties and non-equilibrium dynamics of bright solitary waves in atomic Bose-Einstein condensates in the zero-temperature limit, and we investigate the non-equilibrium dynamics of a driven atomic Bose-Einstein condensate at finite temperature. Bright solitary waves in atomic Bose-Einstein condensates are non-dispersive and soliton-like matter-waves which could be used in future atom-interferometry experiments. Using the mean-field, Gross-Pitaevskii description, we propose an experimental scheme to generate pairs of bright solitary waves with controlled velocity and relative phase; this scheme could form an important part of a future atom interferometer, and we demonstrate that it can also be used to test the validity of the mean-field model of bright solitary waves. We also develop a method to quantitatively assess how soliton-like static, three-dimensional bright solitary waves are; this assessment is particularly relevant for the design of future experiments. In reality, the non-zero temperatures and highly non-equilibrium dynamics occurring in a bright solitary wave interferometer are likely to necessitate a theoretical description which explicitly accounts for the non-condensate fraction. We show that a second-order, number-conserving description offers a minimal self-consistent treatment of the relevant condensate -- non-condensate interactions at low temperatures and for moderate non-condensate fractions. We develop a method to obtain a fully-dynamical numerical solution to the integro-differential equations of motion of this description, and solve these equations for a driven, quasi-one-dimensional test system. We show that rapid non-condensate growth predicted by lower-order descriptions, and associated with linear dynamical instabilities, can be damped by the self-consistent treatment of interactions included in the second-order description.

This thesis reports the observation of interspecies Feshbach resonances in an ultracold mixture of Rb and Cs atoms. A versatile combined magnetic and optical potential has been designed and constructed which is capable of bringing both $ �\rm{Rb}$ and $ {133}\rm{Cs}$ to degeneracy, and reaching high phase-space density in $ �\rm{Rb}$. High phase-space density mixtures are the first step required in the production of ultracold polar molecules, the topic of much current research. The apparatus capitalises on the efficient capture of atoms by a magnetic trap from a magneto-optical trap, and the efficient sympathetic cooling of Cs by Rb therein. Upon transfer to the crossed optical dipole trap condensates in excess of $1\times10 {6}$ $ �\rm{Rb}$ atoms and approximately $1\times10 {5}$ $ {133}\rm{Cs}$ atoms are produced after direct evaporation and gravito-magnetic tilting of the potential. The observation of six interspecies $ �\rm{Rb}$-$ {133}\rm{Cs}$ Feshbach resonances are reported, three of which had only been predicted theoretically, allowing testing and development of the theoretical model. Furthermore, the extrapolation of this model has predicted numerous Feshbach resonances between $ �\rm{Rb}$ and $ {133}\rm{Cs}$, none of which have been experimentally observed prior to this work. The versatile nature of this apparatus is discussed, including the application of the current system to cooling of $ �\rm{Rb}$. Initial experiments observed seven interspecies resonances, including a broad s-wave resonance at a magnetic field of $(644\pm2)$ G which is in excellent agreement with the theoretical prediction. Further work has revealed that fourteen Feshbach resonances exist in the 0-700 G magnetic field range between $ �\rm{Rb}$ and $ {133}\rm{Cs}$ atoms in the $\left|2,+2\right\rangle$ and $\left|3,+3\right\rangle$ states, respectively. Several of these resonances would be ideal for magneto-association of RbCs molecules, prior to transfer to the rovibrational ground-state.