A cold atom experiment can be used to simulate analogous solid-state systems. This provides the bene�t of having a high degree of control over the system parameters and allowing direct detection methods. Disordered transport is one example of where such a system has much to o�er. This thesis concerns the development of a Bose-Fermi mixture experiment for study of two-dimensional optical lattice systems. To achieve single site resolution of the lattice, the experiment makes use of a double microscope set-up. One microscope provides imaging and the second is used to image a spatial light modulator onto the atomic plane. This provides an extremely versatile potential landscape for a trapped cloud. This thesis presents an overview of the set-up of the experiment including progress towards condensation. Particular focus is given to the design and characterisation of the vacuum system and the combined double microscope and spatial light modulator system. The vacuum system design requires a narrow magneto-optical trapping chamber. A novel epoxy sealing technique has been developed, allowing construction of a chamber of just 36mm thickness whilst maintaining high optical access. To provide illumination for the spatial light modulator a technique for homogenising the output of multi-mode �bre has been developed.

The ALICE experiment at the CERN Large Hadron Collider (LHC) will explore a primordial state of matter that existed in the early Universe. Resonance production at the LHC is of great interest in the study of the phase state of hadronic matter known as Quark Gluon Plasma (QGP). Results are presented on the prospects for φ (1020) meson production in pp collisions. A careful analysis of background subtraction methods with particular attention of φ meson production during the first physics run is also presented. A discussion about the discrepancies between different versions of the PYTHIA event generator in charged-particle multiplicity and its implications in φ production is given. An overview of the physics of strongly interacting matter at high energy densities, and the ALICE experimental apparatus is given. A description of the software development of the ALICE trigger system that allows the determination of transmission quality parameters of cables, and the results obtained from bit-error rate measurements are also given. A feasibility study of the electromagnetic process pp → ppe+e- is presented. Results of the potential backgrounds and signals after full reconstruction along with the trigger rate for such measurement of the luminosity is given.

This thesis is an examination of the uses of mean-field theory in problems of the theory of strongly-correlated electronic systems, particularly to the problem of orbital ordering in transition metal oxides. We will apply mean-field theory to various models for orbital ordering of transition metal oxides, and also show that mean-field theory is not as bad an approximation as it might initially seem. We are also interested modelling superconductivity in heavy fermion systems. We conclude from our modelling on transition metal oxides that the mean-field theory we use based on the Stoner criterion will not be adequate to model such complicated phenomena. We propose an alternate mean-field theory based on non-linear fermionic transformations which we introduce. We suggest further improvements in the form of a non-orthogonal transformation, which we also introduce. As a diversion, we model frustrated antiferromagnetism on a pyrochlore lattice. The particular material is Gd\(_2\)Ti\(_2\)O\(_7\). We show that there are many effects in competition with each other. We conclude with a proposed magnetic structure which appears to be a better fit to experimental data than previous suggestions.

Cold atom samples, at temperatures of the order 100 uK, are useful for a wide reaching array of new and exciting technological and scientific endeavours. Atoms are conventionally cooled by Doppler cooling, which relies on the continuous absorption and reemission of photons in a closed optical cycle. This requirement is diffcult to achieve when there are many allowed decay paths for the excited atom, making Doppler cooling only feasible for a handful atoms with simple energy level structures. More exotic energy level structures, such as those found in molecules, are notoriously diffcult to cool. Coherent cooling schemes in comparison, offer advantages such as insensitivity to frequency detuning or a higher number of photon momenta which can be imparted for each spontaneous emission event making them promising candidates for the optical cooling of particles with more general energy level structures. In order to demonstrate these schemes, we have explored the coherent manipulation of an atomic cloud of Rubidium cooled using a two photon Raman resonance. Despite the long spontaneous decay times of such systems, we find a significant decay in the fidelity of the coherent manipulations, which we have characterised using the techniques of Raman spectroscopy, Rabi oscillations, Ramsey interferometry and spin echo. We have found the minimum time constant for the decay in the decoherence to be 2.1fi0:2 ms, which is a result of non-radiative and partially non-stochastic dephasing mechanisms. Due to a high level of decoherence during the spin-echo experiments further investigation is required to determine the exact ratio of stochastic to non-stochastic dephasing

The range of atoms which can be cooled by lasers is limited to those which have a closed two level structure. Several schemes have been proposed which aim to extend this range by using coherent control of the particle momenta, but none have yet been demonstrated. We hope to implement these and other coherent manipulation schemes, and we begin with a system which is well understood and over which we can exert precise control. This thesis covers the design and construction of an experiment to demonstrate coherent manipulation of cold rubidium atoms collected in a magneto-optical trap. The lower hyperfine levels of these cold atoms very closely mimic the ideal two-level atom, and we use carefully crafted laser pulses to prepare, manipulate, and read their quantum state. The hyperfine levels are coupled using two fields whose frequency difference is equal to the hyperfine splitting. The way in which these Raman coupled levels can be used to emulate a two-level atom is explored, and the experimental apparatus used to create and control the driving fields is described in detail. The amplitude, frequency and phase of these fields is programmable, and complex manipulation schemes can be implemented merely by programming a computer. We have observed Raman transitions in the cold rubidium atoms, and the experimental methods used to detect these features amidst large experimental noise are discussed. Although we have not yet seen Rabi oscillations, we are confident that we can now have sufficient control to begin to implement simple interferometric sequences. However, there remain significant challenges if we are to coherently manipulate the momentum, and the prospects for such manipulation are discussed.

No description available.

This thesis describes the trapping and manipulation of ultracold atoms in time-averaged adiabatic potentials (TAAP). The time-averaged adiabatic potential, proposed in [Phys. Rev. Lett. 99, 083001 (2007)], uses resonant radio frequency (rf) radiation to couple the different magnetic substates of a hyperfine level manifold. The resultant dressed states are time-averaged and produce smooth and versatile trapping geometries. More specifically, we apply rf-radiation (MHz) to a quadrupole magnetic field, which results in an ellipsoidal trapping potential for rubidium-87 atoms in the F=1 manifold. This geometry is time-averaged with the help of oscillating (kHz) Helmholtz fields. We develop a convenient loading scheme for the TAAP which uses a standard TOP trap and suffers negligible atom losses and heating. Subsequently we characterize the TAAP trap itself and observe low heating rates and sufficient lifetimes (>3s). Furthermore it is possible to use a second, weaker rf-field to evaporatively cool the atoms to quantum degeneracy [Phys. Rev. A. 81, 031402 (2010)]. This opens up a route for further experiments in this potential: we show how atoms can be trapped in a double well potential and a ring trap geometry. Additionally a process to instigate rotation in these potentials by rotating the polarization of the rf-radiation is developed and implemented. This allows us to impart angular momentum onto the atomic cloud and spin it into a ring.

In this thesis I review the definition of topological quantum field theories through state sums on triangulated manifolds. I describe the construction of state sum invariants of 3-manifolds from a graphical calculus and show how to evaluate the invariants as boundary amplitudes. I review how to define such a graphical calculus through SU(2) representation theory. I then review various geometricity results for the representation theory of SU(2), Spin(4) and SL(2,C), and define coherent boundary manifolds for state sums based on these representations. I derive the asymptotic geometry of the SU(2) based Ponzano-Regge invariant in three dimensions, and the SU(2) based Ooguri models amplitude in four dimensions. As a corollary to the latter results I derive the asymptotic behaviour of various recently proposed spin foam models motivated from the Plebanski formulation of general relativity. Finally the asymptotic geometry of the SL(2,C) based model is derived.

This dissertation studies the dynamics of atomic Bose-Einstein condensates (nEes) and Bose gases in a suddenly modified potential. Firstly, we investigate the correlation between vortex formation and interference in merging Bose-Einstein condensates. This inherent correlation can explain some experiments in which vortices are formed in interfering condensates. Furthermore, we show the interference properties of merging condensates, particularly the relation of interference among colliding, expanding, and merging condensates, which can explain some complex interference phenomena in recent experiments. Secondly, using the truncated Wigner approximation, we investigate the role of quantum fluctuations in different forms on the transport properties of bosonic atoms in a ID optical lattice. The dynamics of transport with respect to quantum fluctuations in the plane-wave modes is distinct from that in the single-harmonic-oscillator modes. The discrepancies are demonstrated in detail. Quantum fluctuations in Bogoliubov modes lead to stronger damping behaviour of the centre-of-mass motion than quantum fluctuations in the plane-wave and single-harmonic-oscillator modes, which is in agreement with the experiment. Thirdly, the role of the relative phase variation and velocity of two low-density condensates, and quantum noise on interference properties are discussed. In particular, the incoherent atoms have significant effect on the interference visibility and microscopic dynamics. Although the interference pattern is not broken by quantum fluctuations, indicating the robust character of this interference, the process of inner correlations and dynamics is very complex and cannot he understood purely with mean-field theory. Finally, we investigate the elementary excitation spectrum and mode functions of a trapped Bose gas by numerically solving the Bogoliubov-De Gennes equation. The characteristic form of the Bogoliubov matrix, determined by the interatomic interactions, and the interaction between atoms and confining potential, specifies excitation spectra and mode functions. The role of these interactions on the properties of spectra and mode functions are shown.

In this thesis, we describe, both semiclassically and quantum mechanically, the single-particle and collective dynamics of electrons and ultracold atoms moving through periodic potentials. Firstly, we explore collective electron dynamics in superlattices with an applied voltage and tilted magnetic field. Single electrons in this system exhibit non-KAM chaotic dynamics. Consequently, at critical field values, coupling between Bloch and cyclotron motion causes delocalisation of the electron orbits, resulting in strong resonant enhancement of the drift velocity. We show that this dramatically affects the collective electron behaviour by inducing multiple propagating charge domains and, consequently, GHz-THz current oscillations with frequencies ten times higher than with no tilted field. Secondly, we study the effect of applying an acoustic wave to the superlattice and find that we can induce high-frequency single electron dynamics that depend critically on the wave amplitude. There are two dynamical regimes depending on the wave amplitude and the electron's initial position in the acoustic wave. Either the electron can be dragged through the superlattice and is allowed to perform drifting periodic orbits with THz frequencies far above the GHz frequencies of the acoustic wave; or, by exerting a large enough potential amplitude, Bloch-like oscillations can be induced, which can cause ultra-high negative differential velocity. We also consider collective electron effects and find that, generally, the acoustic wave drags electrons through the lattice. Additionally, high negative differential drift velocity at the transition between these two single-electron dynamical regimes, induces charge domains in the superlattice that generates extra features in the current oscillations. Finally, we investigate cold atoms in optical lattices driven by a moving potential wave, directly analogous to acoustically-driven superlattices. In this case, we find the same dynamical regimes found in the acoustically driven superlattice. In addition, there are a number a sharp resonant features in the velocity of the atom at critical wave amplitudes and speeds. This could provide a flexible mechanism for transporting atoms to precise locations in a lattice.