Physical Sciences and Mathematics Commons^™

New Aspects Of Optical Coherence And Their Potential For Quantum Technologies, Nathaniel Robert Miller

LSU Doctoral Dissertations

Currently, optical technology impacts most of our lives, from light used in scientific measurement to the fiber optic cables that makeup the backbone of the internet. However, as our current optical infrastructure grows, we discover that these technologies are not limitless. Astronomers find themselves unable resolve stars that are too close to one another. Meanwhile, the internet is always under threat as our computer technology improves and more complex ways to break encryption emerge, threatening our personal information and infrastructure. However, our current optical technology functions on classical principles, and can be easily improved by incorporating our knowledge of quantum …

Optomechanical Quantum Entanglement, Kahlil Y. Dixon

LSU Doctoral Dissertations

As classical technology approaches its limits, exploration of quantum technologies is critical. Quantum optics will be the basis of various cutting-edge research and applications in quantum technology. In particular, quantum optics quite efficacious when applied to quantum networks and the quantum internet. Quantum Optomechanics, a subfield of quantum optics, contains some novel methods for entanglement generation. These entanglement production methods exploit the noise re-encoding process, which is most often associated with creating unwanted phase noise in optical circuits. Using the adapted two-photon formalism and experimental results, we simulate (in an experimentally viable parameter space) optomechanical entanglement generation experiments. These simulations …

On Characterizing Quantum Processes And Detectors, Kevin Valson Jacob

LSU Doctoral Dissertations

In 2009, physicists at the National Institute of Standards and Technology in Colorado, Boulder developed what could arguable be called the first rudimentary quantum computer [1]. The past decade has seen unprecedented improvements in quantum information science culminating in the demonstration of quantum supremacy --- that quantum computers can solve problems that are impractical to be solved on the best supercomputers [2]. This remarkable progress necessitates the development of techniques to characterize the quantum devices that are being developed. In my thesis, I will focus on such devices that manipulate and detect light.

In Chapter 1, I will introduce the …

Quantum Cluster Algebras At Roots Of Unity, Poisson-Lie Groups, And Discriminants, Kurt Malcolm Trampel Iii

LSU Doctoral Dissertations

This dissertation studies quantum algebras at roots of unity in regards to cluster structure and Poisson structure. Moreover, quantum cluster algebras at roots of unity are rigorously defined. The discriminants of these algebras are described, in terms of frozen cluster variables for quantum cluster algebras and Poisson primes for specializations of quantum algebras. The discriminant is a useful invariant for representation theoretic and algebraic study, whose laborious computation deters direct evaluation. The discriminants of quantum Schubert cells at roots of unity will be computed from the two distinct approaches. These methods can be applied to many other quantum algebras.

Multimode Approach To Classical And Quantum Diffraction, Zhihao Xiao

LSU Doctoral Dissertations

I have investigated classical diffraction of optical beams with multimode approach, which is a significant improvement upon the traditional Huygens–Fresnel principle based diffraction theory. I have also investigated quantum diffraction with multimode approach, which describes the behavior of multimode quantum state. Multimode approach to classical and quantum diffraction provides a clear mathematical formalism and is verified by numerical simulations. In addition, I present the work on superconducting qubit and oscillator with time-dependent coupling coefficient, with first order correction with finite qubit energy and schemes based on and π pulses.

Complexity Theory And Its Applications In Linear Quantum Optics, Jonathan Olson

LSU Doctoral Dissertations

This thesis is intended in part to summarize and also to contribute to the newest developments in passive linear optics that have resulted, directly or indirectly, from the somewhat shocking discovery in 2010 that the BosonSampling problem is likely hard for a classical computer to simulate. In doing so, I hope to provide a historic context for the original result, as well as an outlook on the future of technology derived from these newer developments. An emphasis is made in each section to provide a broader conceptual framework for understanding the consequences of each result in light of the others. …

Advances In Quantum Metrology: Continuous Variables In Phase Space, Bryan Tomas Gard

LSU Doctoral Dissertations

This dissertation serves as a general introduction to Wigner functions, phase space, and quantum metrology but also strives to be useful as a how-to guide for those who wish to delve into the realm of using continuous variables, to describe quantum states of light and optical interferometry. We include many of the introductory elements one needs to appreciate the advantages of this treatment as well as show many examples in an effort to make this dissertation more friendly. In the initial segment of this dissertation, we focus on the advantages of Wigner functions and their use to describe many quantum …

Advances In Quantum Optical Metrology And The Establishment Of An Invisible Quantum Tripwire, Steven Blane Mccracken

LSU Doctoral Dissertations

This thesis presents a summary of the foundation and background of the field of quantum optics, and an analysis of some recent discoveries in various fields of which I have aided in furthering investigative research and advancement through publications. Such topics include numerical optimization of generalized quantum states used in phase sensitive quantum metrology, an analysis of object detection through the use of quantum interferometry in the presence of lossy conditions, and the use of the latter technique to propose an invisible quantum tripwire. First is a collaborative effort to numerically optimize quantum optical states for quantum metrological applications. We …

Entanglement, Uncertainty And Relativity In Fundamental Mechanics With An Application In Qkd, Christopher David Richardson

LSU Doctoral Dissertations

In this dissertation I will probe the innate uncertainty of quantum mechanics. After deriving the necessary tools I will tackle Popper's experiment, a long misunderstood thought experiment with recent experimental results. I will then discuss how uncertainty changes when making measurements from different relativistic reference frames and resolve some on the tension between quantum mechanics and relativity. Finally I utilize the practical aspect of quantum uncertainty and describe a practical quantum key distribution scheme.

Studies Of Small Systems In Quantum Information, Sai Vinjanampathy

LSU Doctoral Dissertations

I study two topics in quantum information theory from the perspective of algebra and geometry. The first relates to exploring the geometry of unitary operators for small quantum systems, specifically three-level systems. Such an understanding of the space over which quantum systems evolve is central to understanding the detailed dynamics of quantum systems and to understand the correlation properties of subsystems that compose a given quantum system. The geometry of unitary operators also allows for the calculation of path-dependent phases called geometric phases. These geometric phases are central to understanding a variety of experiments. I present a general technique, called …

Quantum Light For Quantum Technologies, William Nicholas Plick

LSU Doctoral Dissertations

In this thesis we will theoretically investigate three potentially useful physical systems, after first developing the theoretical framework necessary for studying them. First, we will study the multiphoton absorption properties of maximally path entangled number (N00N) states. This is directly relevant to quantum lithography, and beating the Rayleigh diffraction limit. Next, we will develop a new scheme for quantum interferometry: dubbed coherent-light boosted super-sensitive quantum interferometry, which has the potential to reach below the shot noise limit for high photon fluxes, and requires no esoteric detection protocol, or technological elements that have yet to be developed. Finally we propose a …