Ultracold atomic gases can be utilised as extremely sensitive probes of their surrounding environment. In particular, samples of ultracold atoms confined using chip-based microtraps are an ideal tool for mapping electric and magnetic field landscapes. Over the course of this thesis, a new experiment capable of performing surface microscopy using magnetically trapped clouds of cold rubidium-87 atoms has been built. The focus of the work is on the design and construction of the experimental system, which must incorporate many different aspects for manipulating thermal atomic gases, with a view to positioning them at sub-micron distances from special surfaces. This reduced atom-surface separation is necessary for implementing a high resolution, high sensitivity magnetic field sensor with cold atoms. Although current microfabrication techniques easily enable trapping at distances on the order of micrometres, several distance-dependent surface effects - such as the Casimir-Polder force, Johnson-Nyquist noise, and stray potentials - eventually impede magnetic trapping at the sub-micron level. These surface effects can greatly modify the confining potentials, which reduces the trap depth and consequently leads to an additional loss rate of atoms from the trap. We have explored the possibility of using special surfaces such as nano-membranes of silicon nitride and graphene, which have reduced atom- surface interactions, to enable trapping distances at the sub-micron level. A multilayer printed circuit board chip has been designed to form an initial magnetic trap and then transport the cloud of atoms to a desired location over the samples. This chip, along with various samples, is mounted on a custom-made electrical feedthrough designed to make connections to all conductor that are inside the vacuum chamber. The initial cloud of cold atoms can then be prepared in the central region of the chip and delivered to the location of the samples on either side. The experimental system is able to routinely capture over 10^8 rubidium-87 atoms at a temperature of 80 micro-Kelvin in a magneto-optical trap using a novel scheme of five laser beams. A method is demonstrated for enhancing the atom number in the magneto-optical traps by a factor of two by using laser beams with two slightly different frequencies. Atoms from the magneto-optical trap are then transferred to a purely magnetic trap formed by the wires on the printed circuit board chip. Time-dependent currents in the chip wires then create a dynamic potential, which is shown to successfully transport the atomic sample over a distance of 12 millimetre with minimal atom loss. This thesis describes the development of the apparatus in detail, along with careful characterisation of the cold cloud at various stages of the experimental sequence. Initial results on the long distance atom transport are presented. Finally, the experimental results of the two frequency magneto-optical trap for atom number improvement are discussed.

In this thesis we present a modification of Yang-Mills and Gravity theories both written in terms of gauge connections. In particular gravity is presented in its pure connection formulation realizing a Diffeomorphism Invariant Gauge Theory. The modifications do not change the kinematical content of the theories, but they add an infinite set of new vertices retaining the symmetries of the original Lagrangians without introducing higher derivatives in the equations of motion. These new interactions are chiral, leaving the original Yang Mills and Gravity theories as the only parity-invariant theories in the set. In the Yang-Mills case we proved that at tree level the theory is still constructible via the so-called BCFW recursion relations. Both theories are claimed to be closed under the renormalization group. The Yang-Mills Deformations are indeed proved to be one-loop renormalizable and an explicit diagrammatic computation of the simplest deformation beta-function is given. For gravity a new formulation is introduced that could lead to a similar result at one-loop.

The system identification problem is to estimate dynamical parameters from the output data, obtained by performing measurements on the output fields. We investigate system identification for quantum linear systems. Our main objectives are to address the following general problems: (1) Which parameters can be identified by measuring the output? (2) How can we construct a system realisation from sufficient input-output data? (3) How well can we estimate the parameters governing the dynamics? We investigate these problems in two contrasting approaches; using time-dependent inputs (Sec. 3.7.1 or time-stationary (quantum noise)) inputs (Sec. 3.7.2). In the time-dependent approach, the output fields are characterised by the transfer function. We show that indistinguishable minimal systems in the transfer function are related by symplectic transformations acting on the space of system modes (Ch. 6). We also present techniques enabling one to find a physical realisation of the system from the input-output data. We present realistic schemes for estimating passive quantum linear systems at the Heisenberg limit (Ch. 7) under energy resource constraint. ‘Realistic’ is our primary concern here, in the sense that there exists both experimentally feasible states and practical measurement choices that enable this heightened performance for all passive quantum linear systems. We consider both single parameter and multiple parameter estimation. In the stationary approach, the characteristic quantity is the power spectrum. We define the notion of global minimality for a given power spectrum, and characterise globally minimal systems as those with fully mixed stationary state (Sec. 6.1). The power spectrum depends on the system parameters via the transfer function. Our main result here is that under global minimality the power spectrum uniquely determines the transfer function, so the system can be identified up to a symplectic transformation (see Secs. 6.5, 6.4 6.11). We also give methods for constructing a globally minimal subsystem directly from the power spectrum (see Sec. 6.3). These results hold for pure inputs, we discuss extensions to mixed inputs and the use of additional input channels; using an appropriately chosen input in the latter case ensures that the system is always globally minimal (hence identifiable). Finally, we discuss a particular feedback control estimation problem in Chs. 8 and 9. In general, information about a parameter within a quantum linear system may be obtained at a linear rate with respect to time (in both approaches above); the so-called standard scaling. However, we see that when the system destabilises, so that its system matrix has eigenvalues very close to the imaginary axis, the quantum Fisher information is enhanced, to quadratic (Heisenberg) level. We give feedback methods enabling one to destabilise the system and give adaptive procedures for realising the Heisenberg bounds.

No description available.

In this thesis different routes to the formation of extended two-dimensional polymers via on-surface coupling reactions are presented. Polyphenylene networks formed by the molecules tri-(bromo-phenyl)-benzene via on-surface Ullmann coupling reactions are investigated with scanning tunnelling microscopy. The polyphenylene networks with near complete surface coverage exhibit a vitreous structure. The network is composed of linked molecules forming polygons with four to eight edges. A different set of covalently bound molecular nanostructures can be formed on a surface upon thermal activation of porphyrin building blocks. Porphyrin molecules are covalently linked to form one dimensional chains or extended networks using either Ullmann-type coupling reactions to link brominated phenyl sidegroups, or Glaser-Hay-type coupling to form butadiene links via reaction of two phenyl-ethylene sidegroups. The resulting polymers are investigated with scanning tunnelling microscopy and Raman spectroscopy. In a complementary strand of research it is shown that thin films of C60 can promote adhesion between a gold thin film deposited on mica and a solution-deposited layer of the elastomer polymethyldisolaxane (PDMS). This molecular adhesion facilitates the removal of the gold film from the mica support by peeling and provides a new approach to template stripping which avoids the use of conventional adhesive layers. The fullerene adhesion layers may also be used to remove organic monolayers and thin films as well as two-dimensional polymers such as the porphyrin networks discussed previously. Following the removal from the mica support the monolayers may be isolated and transferred to a dielectric surface by etching of the gold thin film, mechanical transfer and removal of the fullerene layer by annealing/dissolution. The use of this molecular adhesive layer provides a new route to transfer polymeric films from metal substrates to other surfaces. A different set of experiments investigated porphyrin nanorings and their interaction with C60 on a gold surface. Solvent-induced aggregates of nanoring cyclic polymers may be transferred by electrospray deposition to a surface where they adsorb as three dimensional columnar stacks. The observed stack height varies from single rings to three stacked rings. Those stacked layers of cyclic porphyrin nanorings constitute nanoscale receptacles with variable height and diameter which preferentially adsorb sublimed C60 molecules. Using scanning tunnelling microscopy the filling capacity of these nanoring traps is determined, as is the dependence of adsorbate capture on stack height and diameter.

Recent achievements in ultra-cold experiments have made quantum simulation of interacting many-body systems possible in a well controllable environment. Of many candidates as quantum simulators, Rydberg atoms have been extensively utilised due to its exaggerated and fascinating atomic properties. Example includes high susceptibility to electric fields and relatively long life time in comparison to atoms in low-lying states. The tunable interaction between Rydberg atoms have made them even more versatile in simulating quantum many-body systems, e.g. interacting spin-1/2 particles. We will start the thesis by reviewing these properties of Rydberg atoms and explain how they lead to the Rydberg lattice gases that of interest. Following the review of the essential knowledge of Rydberg atoms, we first study the ground states of interacting Rydberg lattice gases in both one-dimension and two-dimensions. The many-body system we are interested in is initially prepared in a Mott-insulator state, with each lattice site containing one atom that is laser coupled to its highly excited Rydberg state. The extremely huge van der Waals interactions between Rydberg atoms at close distance leads to an interesting Rydberg blockade effect. As we shall show, these strong interactions lead to rich phases and critical behaviours in the ground states of the many-body Hamiltonians that describes the systems. The aim of the first three chapters is to analyse these ground states in detail. Having investigated the static properties, we then move on to study the dynamical behaviour of a class of generic spin models which can in principal be realised by Rydberg lattice gases with tunable blockade radius. By deriving an effective master equation, and comparing it to the exact calculation, we will demonstrate how different pure initial states eventually evolve to the same equilibrium state and analysed in detail the time evolution and the steady state.

The liberal and republican traditions of political thought are commonly treated as divergent political-philosophical doctrines which existed in a state irreconcilable opposition in late eighteenth-century France and America. The present study challenges this notion through examining the concept of political neutrality as discussed and expounded in the political and constitutional writings of James Madison and Benjamin Constant. In seeking to account for not only why, but also how, both thinkers endeavoured to construct political systems geared toward securing the production of neutral laws, this thesis explores and highlights the complex interdependent relationship between the liberal and republican philosophical traditions in late eighteenth- and early nineteenth-century political theory. It is argued that in their desire to construct political-constitutional systems tailored toward guaranteeing the materialisation of neutral laws, Madison and Constant incorporated republican, or ‘Real Whig’, concepts into their respective constitutional strategies. Their shared objective, it is shown, was to form limited and neutral states through exploiting the diversity of public opinion in such a way that would render popular sovereignty self-neutralising. More specifically, this thesis suggests that both Madison and Constant placed considerable emphasis on de-legitimising particular justifications for legislative action, and that their respective efforts in this area were motivated by a desire to restrict the legislature to the promotion of objective, and impartially-conceived, accounts of the public good. Thus through examining Madison’s and Constant’s attempts to form neutral states, this thesis challenges the traditional account of the development of modern liberalism through pointing to the existence of an autonomous liberal-republican philosophy in post-revolutionary French and American political thought. It is argued that this hybrid political philosophy – which underpinned the constitutionalisms advanced by both Madison and Constant – had as its principal objective the reconciliation of the practice of popular governance with the restoration and maintenance negative individual liberty. Both thinkers, in other words, exploited republican concepts and institutions in order to realise the distinctly liberal end of forming limited and neutral states.

M.A. / This study focuses on the concept of an open society, a concept that was given currency by the philosopher Karl Popper in his 1945 book, The Open Society and its Enemies. Popper provides five imperatives for an open society: state power must be limited and strictly controlled; the aim of public policy must be the reduction of misery; massive reconstruction must be foresworn in favour of incremental changes, guided by critical feedback from the citizenry; institutions to enable free criticism are essential to an open society; and individualism and diversity must be cherished as the source of a richer and more valuable critique. This study examines the South African Constitution to evaluate the extent to which it, as an institution, contributes to the attainment of a Popperian open society, and concludes that it provides the enabling conditions to attain four out of five of Popper’s imperatives. Where it does not succeed is in providing for incremental social change: on the contrary, it enshrines a vision of a radically reconstructed society. Ironically, that vision seems to have been renounced by the state, which has instead adopted an austere economic policy designed to win global approval. This policy has elicited widespread criticism, as have other government policies. Government response to criticism has been far from the positive acceptance envisaged by Popper, ranging from dismissal to outrage to blatant attempts to silence criticism through regulation or legislation. In the case of criticism from the courts (in the form of judgments against government agencies) response has frequently been non-compliance with court orders, even with Constitutional Court orders. The Constitutional Court represents one of the institutional checks and balances on the state demanded by Popper, having considerable powers of judicial review to guard against the abuse of state power. An evaluation of the Court’s contribution towards the attainment of an open society suggests that initially the Court was somewhat reticent about exerting its powers, to the extent of being taxed by some with undue deference towards government. In recent years, however, the Court has shown signs of increased assertiveness, finding for government on fewer occasions and attaching structural interdicts to its orders. It nonetheless requires something more, if the Constitutional Court is to make the contribution it should towards attaining an open society, and this study concurs with a suggestion that the Court undertake public interest litigation, as other apex courts have done. The open society envisaged by the Constitution (and by Popper) requires that the Constitutional Court be vigilant for abuses of state power, provide an ongoing critique of public policy through its judgments, and even accept its share of responsibility for realising the reconstructive vision portrayed in the Constitution, through actively identifying, investigating and addressing injustices in our society.

Ultracold mixture experiments hold the promise of providing new insights into many-body quantum systems as well as ultracold chemistry and few-body phenomena. The work presented in this thesis dealt with the construction of a new apparatus for the production and study of ultracold gases of fermionic lithium-6 and bosonic caesium-133. These isotopes offer a wide tunability in their interaction strength, both in inter-species and intra-species collisions, through magnetic Feshbach resonances. Additionally, the widely different resonance frequencies of lithium and caesium enables independent control of each of the species. With this apparatus, Bose-Einstein condensates (BEC) containing 10^4 lithium Feshbach molecules are routinely produced. The cooling system for caesium has been developed in parallel and important steps towards producing ultracold caesium gases have been made. An optical dipole trap has been loaded with 2x10^6 caesium atoms and evaporative cooling towards quantum degeneracy can now be pursued. Laser, vacuum, magnetic and control systems have been developed for the implementation of this experiment. Light produced with this laser system was used to laser cool atoms, create conservative dipole traps as well as to provide means of imaging atomic clouds. Additionally, a system to produce strong magnetic fields of up to 1400 G has been established in order to exploit the wide tunability in the atomic interactions. Software that was developed for the computerised control system facilitated the coordination of all the components involved in the experimental sequence. Measurements and calculations that showcase the functionality of relevant parts of the setup are presented in this thesis. In this experiment, lithium and caesium atoms are obtained from a novel type of Zeeman slower and are loaded into a magneto-optical trap (MOT). The system is capable of doing this independently for each of the atomic species as well as sequentially. After the MOT has been loaded with atoms, they are transferred into a conservative far-off-resonance optical dipole trap. By adjusting the interactions between atoms and lowering the depth of the dipole trap, efficient evaporative cooling of lithium was carried out from which a molecular BEC was obtained. Time-of-flight measurements were used to characterise the condensate and study its expansion dynamics.

Magister Legum - LLM