School of Physics - Theses
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ItemErbium for optical modulation and quantum computation( 2017)Erbium (Er) is a lanthanide element, mainly used in its trivalent ionic form (Er3+), as an active dopant in optical devices, for light amplification or generation. The luminescence of Er3+ lies within the conventional wavelength band, 1530-1565 nm, for fiber-optic communication. The low noise, linear response, and stability of the optical gain provided by the Er3+ luminescence are ideal for applications in photonic systems that operate in the fiber-optic frequency. While much research has been done to understand the Er3+ luminescence in various lasing media, few studies have been conducted to tap the potential of Er for applications other than amplifiers or lasers. This thesis delves into two new areas, namely optical modulation and quantum computation, where the Er3+ luminescence may be able to be applied in a novel way. By incorporating Er3+ into a switchable optical material, an optical modulator could potentially be made that is capable of not only switching but also amplifying signal transmission or sustaining the signal intensity from propagation losses. This integrated approach could reduce device footprint and latency for on-chip as well as synchronous applications. Successful integration of Er, however, has never been demonstrated in conventional optical modulators because their reliance on electro-optic effects conflicts with the carrier-sensitive mechanism of the Er3+ luminescence. The compatibility between Er and a recently advocated optical material, namely vanadium dioxide (VO2), is examined in the first part of this thesis. VO2 exhibits a hysteretic, bistable phase transition that is accompanied by a high-contrast optical switching in infrared, including the fiber-optic, wavelength band. The phase transition can be triggered thermally as well as optically. When triggered optically, it can occur in picosecond timescale, making VO2 a promising material for ultrafast optical switching applications. Experimental characterizations of the Er3+ luminescence and the optical switching were performed on selectively prepared thin-film samples of VO2. The Er3+ luminescence could be observed after the samples were implanted with Er and then annealed between 800*C and 1000*C. The optical switching could also be measured in the implanted and annealed samples as they were thermally heated up and then cooled down past the critical temperature of the phase transition. The Er-implanted samples, however, were found to have broader hysteresis and lower switching contrasts than the pure VO2 samples. It is concluded that although Er-implanted VO2 could probably work as a combined optical switch and amplifier, the poorer switching qualities do not guarantee that a device based on the material could provide better utility than a separated system of optical switches and Er amplifiers. The Er3+ luminescence could also be utilized for quantum frequency conversion, for implementation in interconnects that interface superconducting quantum computers to a fiber-optic quantum network. For two superconducting quantum computers to be able to communicate over a fiber-optic quantum network, the frequency of the signals transmitted from either computer needs to be converted into the fiber-optic frequency, and then back into the microwave frequency upon receipt at the other computer. Early proposals suggested that the interconnect be at least comprised of Er3+ ions, a microwave resonator, and an optical resonator. The realization of this system has been attempted recently in basic experiments, but the conversion efficiency was found to be too low. The weak couplings between the Er3+ ions and the two resonators were identified as one of the main reasons for the low conversion efficiency. One way to mitigate the weak coupling in the microwave part is to have a superconducting flux qubit bridge the interaction between the Er3+ ions and the microwave resonator. The second part of this thesis presents a theoretical and simulation study of the dynamics of a coupled system consisting of Er3+ ions, a superconducting microwave resonator, an optical resonator, and a superconducting flux qubit. It is shown that quantum information can be exchanged between the Er3+ ions and the microwave resonator with a high fidelity via the qubit coupling, and the exchange process is controllable by changing the frequency of the qubit. The frequency conversion between the microwave and the optical regime is shown to be infeasible to be realized at the limit where the number of optical excitations (n) is much less than the number of ions (N). A high-efficiency frequency down-conversion is demonstrated to be achievable in the case where there is no decoherence, and both n and N are small. However, the time it takes to complete the down-conversion is very long, leaving the efficiency prone to decoherence. It is argued that for the frequency conversion to be able to be accomplished in a typical decoherent environment, both n and N need to be large. The study of the dynamics, in this case, is left for future research.
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ItemAdvances in atomic resolution imaging using scanning transmission electron microscopy( 2017)Scanning transmission electron microscopy (STEM) is capable of imaging at sub-Ångström resolution, simultaneously acquiring multiple signals resulting from the elastic and inelastic scattering of the electron probe. In this thesis theoretical advances are made, in tandem with experiment, to develop novel imaging techniques in STEM: the characterisation of surface reconstructions using secondary electrons, a method for elemental mapping, a method for studying electric and magnetic fields in a specimen and an investigation of specimen mis-tilt in annular bright-field imaging.
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ItemThe role of thermal scattering in the imaging of condensed matter at atomic resolution( 2014)Transmission electron microscopy is a technique capable of determining specimen composition and structure at atomic resolution. Since the invention of the first microscopes in the 1930’s, a series of instrumentation and theoretical advances have led to a mature field where one can routinely obtain images of individual columns of atoms with high precision. Despite the extraordinary success of the microscope and its prevalence in laboratories around the world, interpretation of experimental images is a non-trivial matter. The strong interaction of electrons with the charged particles making up the target specimen (~10^4 times greater than that for x-rays) results in interesting and complicated scattering dynamics which can make direct interpretation of experimental images difficult. A particularly important scattering mechanism at high incident energies is thermal scattering, whereby the incident electron excites a phonon (that is, a vibrational mode) within the specimen. In this thesis we will present a new model for thermal scattering which affords new physical insights as compared with previous models. In particular the new model distinguishes between elastic and thermal scattering of the fast electron and can predict the individual contributions to the scattered intensity from both types of scattering. We will use this model to gain new insights into the role of thermal scattering in a number of different imaging modes.
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ItemCollective superfluid vortex dynamics and pulsar glitches( 2011)Pulsar glitches offer a way of studying the dynamics of cold, ultradense matter in systems of stellar dimensions, under extremes of density, temperature and magnetisation unattainable on Earth. This thesis aims to build a robust model of pulsar glitches, based on the superfluid vortex unpinning paradigm, which relates the physical parameters of the pulsar interior to the observed distribution of glitch sizes and waiting times (power laws and exponentials respectively). Our modelling efforts draw together knowledge about superfluid vortex dynamics and pinning, garnered from condensed matter and nuclear physics, the observational facts gathered by pulsar astronomers, and the theoretical framework of non-equilibrium stochastic systems, such as those exhibiting self-organised criticality. In each case, we emphasise the necessity of collective mechanisms in triggering avalanche-like vortex unpinning events. We begin by studying the dynamics of superfluid vortices from first principles, using numerical solutions of the Gross-Pitaevskii equation (GPE). We solve the GPE in the presence of a lattice of pinning sites, in a container that is decelerated at a constant rate, mimicking the electromagnetic spin-down torque on a pulsar. The superfluid spins down spasmodically, as vortices unpin and hop between pinning sites when the Magnus force, due to the lag between the superfluid and vortex line velocities, exceeds a threshold. Torque feedback between the superfluid and its container regulates the lag between the superfluid and crust, resulting in abrupt increases in the container angular velocity. We study how the statistics of the sizes and waiting times between spin-up events change with the mean and dispersion of pinning strengths, the electromagnetic spin-down torque, the relative number of vortices compared to pinning sites, and the ratio of the crust and superfluid moment of inertia - all parameters of interest in neutron stars. We find that mean glitch size increases with mean pinning strength and the ratio of the moments of inertia. It is independent of the relative number of pinning sites and vortices, suggesting that vortices move a characteristic distance before repinning, rather than repinning at the next available site. The mean waiting time decreases with the number of pinning sites and vortices, the ratio of the moments of inertia and the spin-down torque, and it increases with the width of the pinning strength distribution. In order to explain the broad range of observed glitch sizes using the vortex unpinning paradigm, a collective unpinning mechanism is required. Using numerical solutions of the GPE, we study how the unpinning of one vortex can cause other vortices to unpin. We identify two knock-on triggers: acoustic pulses emitted as a vortex repins, and the increased repulsive force between vortices locally, when an unpinned vortex approaches its nearest neighbours. In the second half of the thesis, we construct a suite of three large-scale stochastic models of glitches. We are inspired to prosecute this program by similarities between the statistics of archetypal self-organised critical systems, such as earthquakes and sand piles, and those of pulsar glitches. The essential features of the vortex dynamics observed in the GPE simulations are abstracted and condensed into a set of iterative rules that form the basis of automata and analytic glitch models. A cellular automaton model, in which vortices interact with nearest neighbours via the Magnus force, reveals that when all pinning sites are of the same strength, large-scale inhomogeneities in the pinned vortex distribution are necessary to produce a broad range of glitch sizes. In this case, glitch sizes and durations are power-law-distributed, and waiting times obey an exponential distribution. We find no evidence of history-dependent glitch sizes or aftershocks. A coherent noise model, based on a similar model developed to study atom hopping in glasses, in which pinning strength varies from site to site, but the pinned vortex distribution is assumed to be spatially homogeneous, exhibits power-law-distributed glitch sizes. Exponential waiting times are put in by hand, by assuming that the stress released in a glitch accumulates over exponentially-distributed time intervals. A wide range of pinning strengths is needed to find agreement with radio timing data. Mean pinning strength is found to decrease with increasing characteristic pulsar age. Finally, we construct a statistical model that tracks the vortex unpinning rate as a function of the stochastically fluctuating global lag between the superfluid and container. Monte-Carlo simulations and a jump-diffusion master equation reveal that a knock-on mechanism that is finely tuned with respect to the pinning strength, is essential to producing a broad range of glitch sizes. Estimates of the power dissipated in acoustic waves during repinning, and of the strength of the proximity effect, do not meet the fine-tuning criteria. We propose to extend this promising model to include nearest-neighbour interactions in the future, in the hope that this may lessen the need for fine tuning. The non-axisymmetric rearrangement of the superfluid velocity field during a vortex-avalanche-driven glitch is a source of gravitational radiation. We calculate the gravitational wave strain using the characteristic vortex motion observed in the GPE simulations. We set an upper bound on the wave strain of h ~ 10-23 for a glitch resulting from an unpinning avalanche of the maximum observed size. We also estimate the contribution to the stochastic gravitational wave background from the superposition of many glitches from a Galactic neutron star population. We place an upper bound on the signal-to-noise ratio of the background of ~ 10-5 for the Advanced LIGO (Laser Interferometer Gravitational-wave Observatory) detector. Detection of a gravitational wave signal from glitches can teach us about the physics of matter at nuclear densities, from the equation of state to transport coefficients like viscosity.