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Entanglement Generation and Quantum Chemistry: Quantum Mechanics at the Exponential Scale

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Abstract

This thesis concerns two main subjects: the parallelization and applications of a recently developed quantum chemistry method known as heat-bath configuration interaction (Chapter 2) and the generation of entanglement in plasmonically coupled quantum dots (Chapters 3 and 4). Chapter 2 describes the implementation (with a careful eye towards parallelization) and applications of the recently developed heat-bath configuration interaction (HCI) algorithm. HCI is a fast selected configuration interaction plus perturbation theory method for finding the exact energy of small, challenging systems within a given basis. Though it is faster than many alternatives, it is still an exponentially scaling algorithm; careful implementation and the use of parallel computing are necessary to study interesting systems. We describe the important implementation and parallelization details, along with providing performance results. We then apply the method to two interesting systems: solid silicon, as a benchmark for other quantum chemistry methods, and the binding curve of Cr2, which cannot be computed reliably by any of the other state of the art algorithms. Chapter 3 concerns the modeling of the quantum dynamics of two, three, or four quantum dots in proximity to a plasmonic system such as a metal nanoparticle or an array of metal nanoparticles. For all systems, an initial state with only one quantum dot in its excited state evolves spontaneously into a state with entanglement between all pairs of QDs. The entanglement arises from the couplings of the QDs to the dissipative, plasmonic environment. Moreover, we predict that similarly entangled states can be generated in systems with appropriate geometries, starting in their ground states, by exciting the entire system with a single, ultrafast laser pulse. By using a series of repeated pulses, the system can also be prepared in an entangled state at an arbitrary time. Chapter 4 investigates systems of two or more quantum dots interacting with a dissipative plasmonic nanostructure by using a cavity quantum electrodynamics approach with a model Hamiltonian. We focus on determining and understanding system configurations that generate multiple bipartite quantum entanglements between the occupation states of the quantum dots. These configurations include allowing for the quantum dots to be asymmetrically coupled to the plasmonic system. Analytical solution of a simplified limit for an arbitrary number of quantum dots and numerical simulations and optimization for the two- and three-dot cases are used to develop guidelines for maximizing the bipartite entanglements. For any number of quantum dots, we show that through simple starting states and parameter guidelines, one quantum dot can be made to share a strong amount of bipartite entanglement with all other quantum dots in the system, while entangling all other pairs to a lesser degree.

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2018-05-30

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Open Quantum Systems; Quantum Chemistry; Theoretical physics

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Umrigar, Cyrus Jehangir

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Mueller, Erich
Ralph, Daniel C.
Fuchs, Gregory David

Degree Discipline

Physics

Degree Name

Ph. D., Physics

Degree Level

Doctor of Philosophy

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Government Document

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dissertation or thesis

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