 School of Physics  Theses
School of Physics  Theses
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ItemTopological quantum computing with magnetsuperconductor hybrid systemsCrawford, Daniel ( 202311)Developing a practical general purpose quantum computer is this eras moonshot project, enabling fundamental advances in simulating quantum manybody systems, as well as promising new classicalcomputerbeating algorithms with applications in cryptography, meteorology, economics, and logistics. Current quantum processors struggle with short coherence times  meaning that the fragile quantum bits (qubits) break down  resulting in high error rates. Thus complicated or long calculations are prohibitive to run on current devices. Quantum error correction could be the solution, however, many physical qubits are required to encode a single logical qubit. Thus a massive scaling up of hardware is required to realise even a modest number of faulttolerant logical qubits. Over the past twenty years the idea of engineering an inherently faulttolerant, or topological, quantum computer has been developed. In principle, these faulttolerant qubits do not decohere due to a topological protection; the information is distributed across a physical system such that local perturbations do not damage the whole information encoding. Majorana zeromodes, characteristic quasiparticles in topological superconductors, have emerged as a leading candidate for the building blocks of a faulttolerant qubit. Many experimental platforms which might yield Majorana zeromodes have been proposed, but as of writing unambiguous evidence for Majorana zeromodes and topological superconductivity has not been presented in any experiment. Here I study magnetsuperconductor hybrid (MSH) systems, which involve networks of magnetic adatoms assembled on a superconducting surface via lateral atom manipulation using a scanning tunneling microscope tip. These systems are clean and crystalline, and thus are an ideal platform for experiments. I present compelling theoretical and experimental evidence for topological superconductivity in Mn and Fe chains on Nb(110). However, the systems investigated so far experimentally have long localisation lengths, resulting in hybridised Majorana modes. Because these modes cannot be used to build a faulttolerant qubit, I theoretically investigate several extensions to these experiments. I propose constructing quasi onedimensional chains consisting of several rows of magnetic adatoms, with ferromagnetic order in one crystalline direction and antiferromagnetic in the other. I also suggest engineering the Nb(110) surface with an alloy to dramatically increase the Rashba splitting. Both of these proposals are readily accessible in experiment, and could yield nonhybridised Majorana zeromodes. Having established the viability of the platform, I introduce a numerical apparatus for studying manybody nonequilibrium superconducting physics. While this is generic and can be applied to any superconducting problem, here I use it to study topological quantum computing on a MSH platform. I first show that quantum gates can indeed be implemented via braiding Majorana zeromodes. I then show how singlemolecule magnets can be use to initialise and readout MSH qubits. I build on this protocol and introduced a dressed Majorana qubit, which combines an MSH network with singlemolecule magnets. These could be easier to initialise and readout than a conventional Majorana qubit.

ItemNonEquilibrium Processes in Neutron Stars and Ultracold GasesKerin, Alex David ( 202306)From the booms and busts of the economy to the schooling of fish, nonequilibrium phenomena are ubiquitous and appear at all scales. However, nonequilibrium systems have proven infamously difficult to model and understand. In this thesis we present two different of nonequilibrium systems, one classical and one quantum mechanical, and thoroughly investigate their behaviour: (i) the repeated localised mechanical failure of the crust of a spinning down neutron star, and (ii) the dynamics of quenched fewbody quantum systems. As an isolated neutron star spins down the centrifugal force weakens but the gravitational force doesn't change. This results in the crust changing shape and accruing mechanical strain to the point of failure. Mechanical failure locally deforms the crust and dissipates and redistributes strain. This can result in avalanches of further failures as one region of the crust failing may prompt a neighbouring region to fail. The evolving crust is a classical farfromequilibrium system capable of avalanche behaviour like the classic sandpile model. The statistics of crustal failure events are of much interest due to their suggested relevance to transient phenomenon such as glitches or fast radio bursts. We present a cellular automaton designed to describe the evolution of the crust over spin down and the effects of local failure. This automaton describes when and where crustal failures occur and how large they are. Additionally this automaton describes the failureinduced change in the shape of the crust. Using this automaton we find that the star needs to be born spinning over \approx 750 Hz to accumulate sufficient strain to fail at all, that the waitingtimes between subsequent events are distributed as a powerlaw spanning seven orders of magnitude, and that the ellipticities of isolated neutron stars are in the range 10^{13} to 10^{12}, among many other results. It has been suggested that the mechanical failure of the crust is the cause (or result) of a variety of transient phenomena such as glitches or gamma ray bursts. This model provides predictions of the statistical behaviour of crustal failure which can be compared to the observed behaviour of these transients. Additionally, the model describes the shape of the crust and the rotational frequency at all times which allows for the wave strain of emitted gravitational waves to be calculated with implications for searches for continuous gravitational wave sources. Cold quantum gases have attracted a great deal of experimental and theoretical interest thanks to the high degree of experimental control possible over them which makes them excellent testing grounds of quantum theory. Additionally, they are excellent tools for the study of quantum thermalisation. We consider a few interacting particles initially in some equilibrium state and suddenly change (quench) the interaction strength which kicks the system away from equilibrium. Specifically, we consider systems of two and three bodies of arbitrary mass and various particle symmetries interacting via a contact interaction in an isotropic threedimensional harmonic trap. We take particular interest in quenching between the weakly and strongly interacting regimes and the following farfromequilibrium postquench evolution. We describe the nonequilibrium postquench evolution of the system by analytically and semianalytically calculating two observables: the Ramsey signal and the particle separation. We are able to calculate these quantities for the twobody system with arbitrary particle masses for any quench in interaction strength. Additionally, we extend these calculations to threebody systems of two identical fermions and a distinct particle or three identical bosons where the quench is between the strongly and weakly interacting regimes. In the twobody case we find when quenching from weak to strong interactions the particle separation oscillates periodically between \approx0.85a_{\mu} and \approx1.15a_{\mu}, where a_{\mu} is the simple harmonic oscillator lengthscale. For the same quench in the threebody case the particle separation varies depending on the specifics of the system. For the fermionic case the particle separation oscillates periodically, peaking at \approx 2.18a_{\mu} with the mass ratio of the two species determining the minimum separation. For the bosonic case the oscillation is aperiodic. Both the maximum and minimum particle separation are determined by a quantity called the threebody parameter, but particle separation generally oscillates between \approx a_{\mu} and \approx 2a_{\mu}. However, in all cases when quenching from strong to weak interactions the calculations of the particle separation do not converge. This divergence is present whatever the initial state, mass ratio, particle symmetry, etc. and is present only for this particular quench from strong to weak interactions. We investigate possible sources of this divergence and future avenues of research into its causes. Finally, we note that these theoretical predictions of Ramsey signal and particle separation are experimentally testable with current techniques.

ItemErbium for optical modulation and quantum computationLim, Herianto ( 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, 15301565 nm, for fiberoptic 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 fiberoptic 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 onchip as well as synchronous applications. Successful integration of Er, however, has never been demonstrated in conventional optical modulators because their reliance on electrooptic effects conflicts with the carriersensitive 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 highcontrast optical switching in infrared, including the fiberoptic, 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 thinfilm 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 Erimplanted samples, however, were found to have broader hysteresis and lower switching contrasts than the pure VO2 samples. It is concluded that although Erimplanted 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 fiberoptic quantum network. For two superconducting quantum computers to be able to communicate over a fiberoptic quantum network, the frequency of the signals transmitted from either computer needs to be converted into the fiberoptic 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 highefficiency frequency downconversion 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 downconversion 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.

ItemAdvances in atomic resolution imaging using scanning transmission electron microscopyBrown, Hamish Galloway ( 2017)Scanning transmission electron microscopy (STEM) is capable of imaging at subÅngström 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 mistilt in annular brightfield imaging.

ItemThe role of thermal scattering in the imaging of condensed matter at atomic resolutionForbes, Benjamin David ( 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 nontrivial matter. The strong interaction of electrons with the charged particles making up the target specimen (~10^4 times greater than that for xrays) 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.

ItemCollective superfluid vortex dynamics and pulsar glitchesWARSZAWSKI, LILA ( 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 nonequilibrium stochastic systems, such as those exhibiting selforganised criticality. In each case, we emphasise the necessity of collective mechanisms in triggering avalanchelike vortex unpinning events. We begin by studying the dynamics of superfluid vortices from first principles, using numerical solutions of the GrossPitaevskii 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 spindown 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 spinup events change with the mean and dispersion of pinning strengths, the electromagnetic spindown 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 spindown 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 knockon 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 largescale stochastic models of glitches. We are inspired to prosecute this program by similarities between the statistics of archetypal selforganised 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, largescale inhomogeneities in the pinned vortex distribution are necessary to produce a broad range of glitch sizes. In this case, glitch sizes and durations are powerlawdistributed, and waiting times obey an exponential distribution. We find no evidence of historydependent 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 powerlawdistributed glitch sizes. Exponential waiting times are put in by hand, by assuming that the stress released in a glitch accumulates over exponentiallydistributed 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. MonteCarlo simulations and a jumpdiffusion master equation reveal that a knockon 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 finetuning criteria. We propose to extend this promising model to include nearestneighbour interactions in the future, in the hope that this may lessen the need for fine tuning. The nonaxisymmetric rearrangement of the superfluid velocity field during a vortexavalanchedriven 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 ~ 1023 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 signaltonoise ratio of the background of ~ 105 for the Advanced LIGO (Laser Interferometer Gravitationalwave 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.