School of Physics - Theses
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ItemTopological quantum computing with magnet-superconductor hybrid systems( 2023-11)Developing a practical general purpose quantum computer is this eras moonshot project, enabling fundamental advances in simulating quantum many-body systems, as well as promising new classical-computer-beating 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 fault-tolerant logical qubits. Over the past twenty years the idea of engineering an inherently fault-tolerant, or topological, quantum computer has been developed. In principle, these fault-tolerant 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 zero-modes, characteristic quasiparticles in topological superconductors, have emerged as a leading candidate for the building blocks of a fault-tolerant qubit. Many experimental platforms which might yield Majorana zero-modes have been proposed, but as of writing unambiguous evidence for Majorana zero-modes and topological superconductivity has not been presented in any experiment. Here I study magnet-superconductor 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 fault-tolerant qubit, I theoretically investigate several extensions to these experiments. I propose constructing quasi one-dimensional 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 non-hybridised Majorana zero-modes. Having established the viability of the platform, I introduce a numerical apparatus for studying many-body 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 zero-modes. I then show how single-molecule 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 single-molecule magnets. These could be easier to initialise and readout than a conventional Majorana qubit.
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ItemNon-Equilibrium Processes in Neutron Stars and Ultracold Gases( 2023-06)From the booms and busts of the economy to the schooling of fish, non-equilibrium phenomena are ubiquitous and appear at all scales. However, non-equilibrium systems have proven infamously difficult to model and understand. In this thesis we present two different of non-equilibrium 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 few-body 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 far-from-equilibrium 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 failure-induced 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 waiting-times between subsequent events are distributed as a power-law 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 three-dimensional harmonic trap. We take particular interest in quenching between the weakly and strongly interacting regimes and the following far-from-equilibrium post-quench evolution. We describe the non-equilibrium post-quench evolution of the system by analytically and semi-analytically calculating two observables: the Ramsey signal and the particle separation. We are able to calculate these quantities for the two-body system with arbitrary particle masses for any quench in interaction strength. Additionally, we extend these calculations to three-body 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 two-body 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 length-scale. For the same quench in the three-body 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 three-body 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.