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dc.contributor.advisorLusk, Mark T.
dc.contributor.authorDeWolf-Moura, Tyjal
dc.date.accessioned2022-11-09T17:42:26Z
dc.date.available2022-11-09T17:42:26Z
dc.date.issued2022
dc.identifierDeWolfMoura_mines_0052N_12435.pdf
dc.identifierT 9379
dc.identifier.urihttps://hdl.handle.net/11124/15470
dc.descriptionIncludes bibliographical references.
dc.description2022 Summer.
dc.description.abstractDespite the attention it has commanded, the resources it has garnered, and the promising theoretical and technological milestones it has passed, quantum computing is in its infancy. A wide range of paradigms are currently being explored, motivated by the need to strike a balance between controllable interactions within the system and isolation from interactions with the environment. Within each of these, strategies that exploit geometric holonomies to store and process information seem especially promising, because they offer a measure of protection against environmental degradation. This tactic has yet to receive much attention for optical quantum computing however. In fact, there is a dearth of information associated with the geometric phase accumulation of entangled photon states|a linchpin for carrying out universal holonomic quantum logic. A theoretical investigation has therefore been carried out that elucidates the relationship between photon entanglement and geometric phase. While intended to be helpful to quantum computing, the focus is on basic science. A particularly simple setting is chosen in which photons propagate along an axis while being laterally confined by a harmonic trap. Treating the propagation axis as time, linear combinations of two-dimensional modes are used to construct optical vortices that orbit about the trap center. Two-photon entangled states are created in terms of these, and the geometric phase is calculated over a single, shared orbital period. This setting makes it possible to scrutinize the relationship between the degree of entanglement and the geometric phase accumulated. Attention is focused on the Geometric Phase of Entanglement (GPE), defined as the geometric phase above and beyond that accumulated by each single-photon state independently. General requirements were identified for which a GPE is supported. A set of especially tractable problems were then explored to show how the GPE is influenced by vortex tilt, orbit radius, and degree of entanglement. The insights obtained comprise a foundation for subsequent experimental investigations. Towards that end, particular attention was also given to explain how the requisite two-photon states can be produced and to identify two physical settings for which the harmonic trap can be realized: a sequence of cylindrical lenses; and multi-mode dielectric fibers.
dc.format.mediumborn digital
dc.format.mediummasters theses
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado School of Mines. Arthur Lakes Library
dc.relation.ispartof2022 - Mines Theses & Dissertations
dc.rightsCopyright of the original work is retained by the author.
dc.subjectBerry phase
dc.subjectentanglement
dc.subjectgeometric phase
dc.subjectoptics
dc.subjectquantum computing
dc.subjectvortices
dc.titleGeometric phase of entanglement for non-adiabatic, two-photon optical vortex evolution in a dielectric trap
dc.typeText
dc.date.updated2022-11-05T04:06:43Z
dc.contributor.committeememberEley, Serena
dc.contributor.committeememberGong, Zhexuan
dc.contributor.committeememberSiemens, Mark
thesis.degree.nameMaster of Science (M.S.)
thesis.degree.levelMasters
thesis.degree.disciplinePhysics
thesis.degree.grantorColorado School of Mines


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