Thesis and Dissertation Defenses
Modeling lithographic quantum dots and donors for quantum computation and simulation
Presented by Mitchell Brickson
Over the last few decades, improvements in the fabrication of nanoscale semiconductor devices have made it possible to scale classical computing technologies to hundreds of billions of transistors per device while also enabling the control of individual electrons and holes. During the same time, algorithms that utilize quantum mechanical effects have been developed that promise to outperform classical computers at certain tasks, as long as quantum computers can be built that will implement them. This dissertation contributes to the understanding of the quantum dot technologies that have been enabled by classical microelectronics, particularly in pursuit of using them as qubits or components of analog quantum simulators. The tools that we develop and use in this pursuit are themselves computational. We have created a numerical framework for modeling quantum dots and related systems, capable of being used in the design and interpretation of experiments on real devices. We describe the details of this framework and apply it to three distinct foci.
Our first focus is on few-hole quantum dots in germanium. We use discontinous Galerkin methods to discretize and solve the equations of a highly detailed k·p model that describes these systems, enabling a better understanding of experimental magnetospectroscopy results. We confirm the expected anisotropy of single-hole g-factors and describe mechanisms by which different orbital states have different g-factors. Building on this, we show that the g-factors in Ge holes are sufficiently sensitive to details of the device electrostatics that magnetospectroscopy data can be used to make a prediction of the underlying confinement potential. The second focus is on designing quantum dot systems for the analog quantum simulations of impurity models. This involves implementing new methods for calculating the properties of open systems and a proposal for measuring impurity Hamiltonian parameters. The final focus is on using Green’s function methods to explore the transport properties of donor arrays fabricated using atomic-precision advanced manufacturing. We simulate bias spectroscopy experiments on a one-dimensional chain of phosphorus donor atoms in silicon, and the manner in which experimental signatures change in the presence of experimentally-corroborated imperfect dopant incorporation.
1:30 pm, Wednesday, November 1, 2023
PAIS-1160, PAIS
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