Physics - Masters by Research Theses

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    Time in quantum mechanics and the Page-Wootters formalism
    (University College Cork, 2023) De Rosa, Guido; Ruschhaupt, Andreas
    This work relates to the "problem of time", the difficulties of which represent a classic problem in the foundations of quantum mechanics. It can be traced back to the argument, by Wolfgang Pauli, on the impossibility of defining time as a quantum observable, due to contradictions related to the spectrum of energy (1933). A number of models, aimed at overcoming such difficulties, have been developed over the decades, and are reviewed in the present work. Particular attention is paid to the theoretical framework first proposed by Page and Wootters in 1983 (later improved by Lloyd, Giovannetti and Maccone and others), where time and unitary evolution only emerge in terms of entanglement between non-interacting subsystems of an otherwise stationary "universe'", and where one of the subsystems acts as a "clock'" for the `"rest" of it. Discrete clocks, within the framework, are implemented, using existing results related to quantum systems described by finite-dimensional Hilbert spaces. The formalism is then applied to some simple quantum systems, and a numerical comparison is performed between the Page--Wootters model and the predictions of "ordinary'" quantum mechanics. The Page and Wootters formalism is also applied to non-unitary systems, such as those modeled in absorption theories of time-of-arrival at a particle detector. A comparison is made between the predictions of the two models as well. The case of a differing result opens the way to the potential of an experimental verification. Future lines of research may cover a broader phenomenology, and include a relativistic extension, which is briefly introduced.
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    Investigating the magnetic fields of high-velocity outflows from active galactic nuclei
    (University College Cork, 2021-08-30) Richardson, Frederick; Gabuzda, Denise; Irish Research Council
    The focus of my M.Sc. degree was the magnetic fields of the jets of Active Galactic Nuclei (AGNs). The exact mechanism for the high levels of collimation in AGN jets is poorly understood. Theoretical models suggest that the collimation of jets is at least partially the result of a helical magnetic field. The primary aim of this thesis is to search for evidence of this structure. For such a magnetic field it is expected to find a Faraday rotation measure gradient transverse to the jet, an increase in fractional polarisation towards the jet edges, and possibly a "spine-sheath" polarisation angle structure. AGN jets that feature more than one of these criteria mentioned may host helical magnetic fields. Observations obtained in 2017 and 2019 of a sample of 16 AGNs (BL Lac objects) were analysed at four radio wavelengths: 6, 13, 17, and 21 cm. The data for these observations were obtained with the "Very Long Baseline Array" of ten radio telescopes spread across the United States. These were the first data of this kind for these AGNs. Observations at multiple radio wavelengths are needed to construct rotation measure maps and detect the presence of a helical or toroidal magnetic field. Eleven of the 16 BL Lac objects host convincing transverse rotation measure gradients with statistical significances greater than 3σ. Two sources ( J0738+1742 and J2202+4216) showed an increase in fractional polarisation towards both edges of the jet as well as a spine-sheath structure. In addition, J0748+2400, J0958+6533, J1800+7828, J1806+6949, J1824+5651, J2005+7752, and J2202+4216 had the EVPA and fractional polarisation structure discussed earlier which strengthens the argument for these jets possibly having helical fields. A secondary objective of my research was to compare my results with the jet structures of these AGNs observed at four wavelengths between 18 and 22 cm at two earlier dates in 2004 and 2010. The morphology, polarisation structure outside the core, and fractional polarisation remained approximately constant. Analogous statistically significant Faraday rotation measure gradients were found at these earlier dates in J0050-0929, J1806+6949, and J1824+5651, and evidence for transverse RM gradient reversals was found for J0818+4222, J0825+0309, J1800+7828, and J2202+4216. The reversal of the direction of a transverse RM gradient with distance from the core or time could result from a nested helical field structure, with the toroidal components of the helical fields being in opposite directions in the inner and outer regions of helical field.
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    Design of bent quantum waveguides via shortcuts to adiabaticity
    (University College Cork, 2020-12) Odelli, Manuel; Ruschhaupt, Andreas
    Quantum waveguides are one of the key components in the developement of quantum technologies that experienced a new surge in popularity in recent years. In quantum computers, quantum particles have to be moved between different sites on a quantum chip through waveguides. The progressive miniaturization of quantum chips requires the waveguides to follow certain paths and so they need to be bent in order to be accomodated onto the chip. If the bending is too abrupt, instabilities are introduced in the system, possibly causing reflection and consequently data loss. This difficulty is usually overcome by adopting the adiabatic approach: the parameter representing the bending needs to vary gently along the waveguide, to prevent disruptive effects. This method, however, cannot be applied in many settings, in particular the ones that need a high degree of compactness. Thus, a new approach that would take into account all the different requirements is needed. ``Shortcuts to Adiabaticity" (STA) offers the right platform to improve on adiabatic processes and in this thesis we will apply a protocol based on STA to maximize particle transmission fidelity in geometries where the adiabatic approach cannot be employed.
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    Analysing curved optical waveguides using the finite difference beam propagation method
    (University College Cork, 2020-09-01) Murphy, Tommy; Peters, Frank H.; Science Foundation Ireland
    Photonic integrated circuits (PICs) integrate optical components on a single semiconductor chip. As time has progressed, advances have been made allowing the components of these PICs to become smaller and smaller. It is now possible to place many of these components on a single PIC. As these components can contain, or be connected by, bending waveguides, it is desirable to make these waveguide bends with as small a radius of curvature as possible to allow many components to fit on the single PIC. Unfortunately, as the radius of curvature decreases, the power loss through the bend increases due to the waveguide’s fundamental mode shifting towards the outside of the bend, causing large loss from the transition between the straight and curved waveguides. The power from the shifted mode also leaks as the fields propagate through the bend. Therefore, the aim of this thesis was to reduce the loss caused by these bends at small radii of curvature, allowing the bends to take up less space on a PIC. This involved designing the waveguide bends to have curvature profiles other than the conventional circular waveguide bend. The propagating fields through the bends were then analysed by numerical simulations using a program utilising the 3D finite difference beam propagation method, which was created and optimised over the course of the research, to investigate if the different curvature profiles could reduce the loss caused by bends in ridge waveguides. It was found that much lower loss could be achieved for curved deep-etched ridge waveguides with small radii of curvature by designing the bend to have a section where the curvature of the waveguide linearly changes.