Physical Sciences and Mathematics Commons^™

Quantum Chaos, Integrability, And Hydrodynamics In Nonequilibrium Quantum Matter, Javier Lopez Piqueres

Doctoral Dissertations

It is well-known that the Hilbert space of a quantum many-body system grows exponentially with the number of particles in the system. Drive the system out of equilibrium so that the degrees of freedom are now dynamic and the result is an extremely complicated problem. With that comes a vast landscape of new physics, which we are just recently starting to explore. In this proposal, we study the dynam- ics of two paradigmatic classes of quantum many-body systems: quantum chaotic and integrable systems. We leverage certain tools commonly employed in equilibrium many-body physics, as well as others tailored to the …

Design And Fabrication Of A Trapped Ion Quantum Computing Testbed, Christopher A. Caron

Masters Theses

Here we present the design, assembly and successful ion trapping of a room-temperature ion trap system with a custom designed and fabricated surface electrode ion trap, which allows for rapid prototyping of novel trap designs such that new chips can be installed and reach UHV in under 2 days. The system has demonstrated success at trapping and maintaining both single ions and cold crystals of ions. We achieve this by fabricating our own custom surface Paul traps in the UMass Amherst cleanroom facilities, which are then argon ion milled, diced, mounted and wire bonded to an interposer which is placed …

Modified Geometries, Clifford Algebras And Graphs: Their Impact On Discreteness, Locality And Symmetr, Roma Sverdlov

Mathematics & Statistics ETDs

In this dissertation I will explore the question whether various entities commonly used in quantum field theory can be “constructed". In particular, can spacetime be “constructed" out of building blocks, and can Berezin integral be “constructed" in terms of Riemann integrals.

As far as “constructing" spacetime out of building blocks, it has been attempted by multiple scientific communities and various models were proposed. But the common downfall is they break the principles of relativity. I will explore the ways of doing so in such a way that principles of relativity are respected. One of my approaches is to replace points …

The Future Between Quantum Computing And Cybersecurity, Daniel Dorazio

Williams Honors College, Honors Research Projects

Quantum computing, a novel branch of technology based on quantum theory, processes information in ways beyond the capabilities of classical computers. Traditional computers use binary digits [bits], but quantum computers use quantum binary digits [qubits] that can exist in multiple states simultaneously. Since developing the first two-qubit quantum computer in 1998, the quantum computing field has experienced rapid growth.

Cryptographic algorithms such as RSA and ECC, essential for internet security, rely on the difficulty of complex math problems that classical computers can’t solve. However, the advancement of quantum technology threatens these encryption systems. Algorithms, such as Shor’s, leverage the power …

Overcoming Atmospheric Effects In Quantum Cryptography, Brian Joseph Rollick

Doctoral Dissertations

Quantum Computers will have the potential to greatly assist us in problems such as searching, optimization and even drug discovery. Unfortunately, among these newfound capabilities is one which allows one to break RSA encryption in orders of magnitude less time. One promising countermeasure to secure our communication today and in the future is the one time pad, although it is very difficult to generate and distribute. Quantum Key Distribution offers a practical method for two authenticated parties to generate a key. Whereby the parties, Alice and Bob, share quantum states and use physical laws to place an upper bound on …

Circulation Transfer Between Adjacent Target Bose-Einstein Condensates, Charles B. Henry

Honors College Theses

We propose an atomtronic rotation sensor design that consists of an array of Bose-Einstein Condensates (BECs) that are confined in a double-target-array potential. The rotation sensor's purpose is to measure the speed of the rotating frame, with respect to the “fixed stars", the sensor rests in. The atomtronic system is an ultracold gas of sodium atoms that have been compressed by laser light into a thin quasi-2D horizontal plane and further confined in the horizontal plane by a double-target-array potential. A target BEC is a combination of disk BEC that is surrounded by a ring BEC. A double-target BEC is …

Automation Of The Transition Identification Procedure For Trapping Rubidium Atoms In A Magneto-Optical Trap, Michael P. Fletcher

Physics

The words “quantum computer” often conjure images of science fiction and unrealistic technology from an impossible future. Some may even believe that they aren’t real or are only theoretical. The truth is that quantum computers are real, tangible systems with real life uses and rooted in credible scientific research. Today, many groups of scientists collaborate on research into better ways of implementing and improving quantum computing techniques. This paper will be addressing the systems required and phenomena used to achieve neutral atom trapping for quantum computation. This thesis will outline the physical phenomena involved with the frequency tuning process for …

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 …

Magnetic Microscopy And Search For Exotic Interaction Detection With Color Centers In Diamond, Nathaniel Ristoff

Physics & Astronomy ETDs

Nitrogen vacancy (NV) centers have been used extensively for the measurement of magnetic fields in applications of geology, biology, medicine, and fundamental physics. In regard to fundamental physics, NV centers offer a unique opportunity to test potential velocity dependant spin-spin interactions as well as velocity-spin interactions at the micron scale. In regards to magnetic materials, NV centers offer a platform to investigate magnetic properties of nanoparticles in an individual, but highly parallelized measurement. In this work, an experiment is proposed to measure a potential fundamental interaction between spins, mediated by an integer spin boson. These velocity dependent interactions will couple …

Solving Chromatic Number With Quantum Search And Quantum Counting, David Lutze

Master's Theses

This thesis presents a novel quantum algorithm that solves the Chromatic Number problem. Complexity analysis of this algorithm revealed a run time of O(2^n/2n²(log2n)²). This is an improvement over the best known algorithm, with a run time of 2ⁿn^O(1) [1]. This algorithm uses the Quantum Search algorithm (often called Grover's Algorithm), and the Quantum Counting algorithm. Chromatic Number is an example of an NP-Hard problem, which suggests that other NP-Hard problems can also benefit from a speed-up provided by quantum technology. This has wide implications as many real world problems can …

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 …

Quantum Optics, Entanglement, And Bell's Theorem, Andrew D. Poverman

Senior Projects Spring 2021

The field of quantum optics provides a wonderful setting in which to study fundamental aspects of quantum mechanics such as entanglement, Bell's theorem, and non-locality. This thesis presents theoretical discussions of qubits, entanglement, and Bell's theorem in addition to experimental discussions on the nature of photons, creating entangled states using Spontaneous Parametric Down-Conversion (SPDC), and a Bell Test with polarization entangled photons. The experimental sections are written to be useful as instructions for one to conduct these experiments on their own. By doing these experiments, one will gain familiarity with quantum optics experiments as well as a firmer grasp on …

Qwasi: The Quantum Walk Simulator, Warren V. Wilson

Theses and Dissertations

As quantum computing continues to evolve, the ability to design and analyze novel quantum algorithms becomes a necessary focus for research. In many instances, the virtues of quantum algorithms only become evident when compared to their classical counterparts, so a study of the former often begins with a consideration of the latter. This is very much the case with quantum walk algorithms, as the success of random walks and their many, varied applications have inspired much interest in quantum correlates. Unfortunately, finding purely algebraic solutions for quantum walks is an elusive endeavor. At best, and when solvable, they require simple …

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 Entanglement Of One-Dimensional Spinless Fermions, Emanuel Casiano-Diaz

Graduate College Dissertations and Theses

The constituents of a quantum many-body system can be inextricably linked, a phenomenon known as quantum entanglement. Entanglement can be used as a resource for quantum computing, quantum communication and detecting phase transitions, among others. The amount of entanglement can be quantified via the von Neumann and Rényi entropies, which have their origins in information theory.

In this work, the quantum entanglement between subsystems of a one dimen- sional lattice model of fermions is quantified. The von Neumann and Rényi entropies were calculated for two types of subsystems. In the first study, the subsystems were treated as two subsets of …

An Introduction To Supersymmetric Quantum Mechanics, Vincent R. Siggia

Theses and Dissertations

In this thesis, the general framework of supersymmetric quantum mechanics and the path integral approach will be presented (as well as the worked out example of the supersymmetric harmonic oscillator). Then the theory will be specialized to the case of supersymmetric quantum mechanics on Riemannian manifolds, which will start from a supersymmetric Lagrangian for the general case and the special case for S2. Afterwards, there will be a discussion on the superfield formalism. Concluding this thesis will be the Hamiltonian formalism followed by the inclusion of deforma- tions by potentials.

The Entropic Dynamics Approach To The Paradigmatic Quantum Mechanical Phenomena, Susan Difranzo

Legacy Theses & Dissertations (2009 - 2024)

Standard Quantum Mechanics, although successful in terms of calculating and predicting

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.

From The Circle To The Square: Symmetry And Degeneracy In Quantum Mechanics, Dahyeon Lee

Honors Papers

The relationship between degeneracy and symmetry in quantum mechanics is explored using two dimensional infinite potential wells with boundaries |x|^n + |y|^n = an for n = 2, whose limiting cases are circular (n = 2) and square (n ¿ 8) well. Analytic solutions for the circular and square cases are derived from separation of variables. Boundary element method (BEM) is a numerical method that solves PDEs using boundary conditions. The BEM is used to solve potential well problems. The method is first tested by comparing numerical solutions with analytic solutions for the circular and square wells. For the ground …

Probing Symmetry And Disorder Effects In The Fractional Quantum Hall States Of The Second Landau Level, Ethan I. Kleinbaum

Open Access Dissertations

Electrons confined to two dimensions, cooled to cryogenic temperatures, and placed in a strong perpendicular magnetic field exhibit a set of ground states referred to as the fractional quantum Hall states (FQHS). The FQHSs forming in the region called the second Landau level are some of the most exciting states as several theories predict that they are very different from the well understood FQHS in the lowest Landau level. Nonetheless, the nature of these FQHSs continue to evade understanding. In this thesis, a unique ultra-low temperature setup is used to examine the FQHSs of the second Landau level in regimes …

Quantum Coherence And Entanglement In Open Quantum Systems, Yiteng Zhang

Open Access Dissertations

We humans always want to believe that we can overpower nature. However, the reality is that nature outperforms humans in many aspects. Animals' abilities to navigate/orient and photosynthesis are two excellent examples in these aspects. However, the mechanisms underlying them are still unknown. For decades, scientists and researchers have made a lot of efforts to reveal these mysteries in nature.

Recently, quantum coherence and entanglement are believed to play a crucial role in such biological systems–avian compass and photosynthesis. Thus, nature might know more tricks to utilize quantum mechanics than humans. Studies on the mechanisms underlying avian compass and photosynthesis …

Simulation Of Nuclear Fusion Using A One Dimensional Particle In Cell Method, Steven T. Margell

Cal Poly Humboldt theses and projects

In this thesis several novel techniques are developed to simulate fusion events in an isotropic, electrostatic three-dimensional Deuterium-Tritium plasma. These techniques allow us to accurately predict three-dimensional collision events with a one-dimensional model while simultaneously reducing compute time via a nearest neighbor algorithm. Furthermore, a fusion model based on first principles is developed that yields an average fusion reactivity which correlates well with empirical results.

Photovoltaics: An Investigation Into The Origins Of Efficiency On All Scales, Jeremy Alexander Bannister

Senior Projects Spring 2016

This project is comprised of a set of parallel investigations, which share the common mo- tivation of increasing the efficiency of photovoltaics. First, the reader is introduced to core concepts of photovoltaic energy conversion via a semi-classical description of the phys- ical system. Second, a key player in photovoltaic efficiency calculations, the exciton, is discussed in greater quantum mechanical detail. The reader will be taken through a nu- merical derivation of the low-energy exciton states in various geometries, including a line segment, a circle and a sphere. These numerical calculations are done using Mathematica, a computer program which, due to …

Scattering Amplitudes In Flat Space And Anti-De Sitter Space, Savan Kharel

Doctoral Dissertations

We calculate gauge theory one-loop amplitudes with the aid of the complex shift used in the Britto- Cachazo-Feng-Witten (BCFW) recursion relations of tree amplitudes. We apply the shift to the integrand and show that the contribution from the limit of infinite shift vanishes after integrating over the loop momentum, with a judicious choice of basis for polarization vectors. This enables us to write the one-loop amplitude in terms of on-shell tree and lower-point one-loop amplitudes. Some of the tree amplitudes are forward amplitudes. We show that their potential singularities do not contribute and the BCFW recursion relations can be applied …

Nonlocal Polarization Interferometry And Entanglement Detection, Brian P. Williams

Doctoral Dissertations

At present, quantum entanglement is a resource, distributed to enable a variety of quantum information applications such as quantum key distribution, superdense coding, and teleportation. Necessarily, the distribution and characterization of entanglement is fundamental to its application. This dissertation details three research efforts to enable nonlocal entanglement detection, distribution, and characterization. Foremost of these efforts, we present the theory and demonstration of a nonlocal polarization interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer’s unique correlation dependence on the anti-diagonal elements of the density matrix, which have distinct bounds for separable states …

Algebraic Semi-Classical Model For Reaction Dynamics, Tim Glenn Wendler

Theses and Dissertations

We use an algebraic method to model the molecular collision dynamics of a collinear triatomic system. Beginning with a forced oscillator, we develop a mathematical framework upon which inelastic and reactive collisions are modeled. The model is considered algebraic because it takes advantage of the properties of a Lie algebra in the derivation of a time-evolution operator. The time-evolution operator is shown to generate both phase-space and quantum dynamics of a forced oscillator simultaneously. The model is considered semi-classical because only the molecule's internal degrees-of-freedom are quantized. The relative translation between the colliding atom and molecule in an exchange reaction …

Isotropic Oscillator Under A Magnetic And Spatially Varying Electric Field, David L. Frost Mr., Frank Hagelberg

Undergraduate Honors Theses

We investigate the energy levels of a particle confined in the isotropic oscillator potential with a magnetic and spatially varying electric field. Here we are able to exactly solve the Schrodinger equation, using matrix methods, for the first excited states. To this end we find that the spatial gradient of the electric field acts as a magnetic field in certain circumstances. Here we present the changes in the energy levels as functions of the electric field, and other parameters.

Hilbert Space Theory And Applications In Basic Quantum Mechanics, Matthew Gagne

Mathematics

We explore the basic mathematical physics of quantum mechanics. Our primary focus will be on Hilbert space theory and applications as well as the theory of linear operators on Hilbert space. We show how Hermitian operators are used to represent quantum observables and investigate the spectrum of various linear operators. We discuss deviation and uncertainty and briefly suggest how symmetry and representations are involved in quantum theory.

Parsimony And Quantum Mechanics: An Analysis Of The Copenhagen And Bohmian Interpretations, Jhenna Voorhis

Scripps Senior Theses

Parsimony, sometime referred to as simplicity, is an effective criterion of theory choice in the case of Quantum Mechanics. The Copenhagen and Bohmian interpretations are rival theories, with the Bohmian interpretation being more parsimonious. More parsimonious theories have a higher probability of being true than less parsimonious rivals. The Bohmian interpretation should thus be preferred on these grounds.

The Violation Of Bell's Inequality In A Deterministic But Nonlocal Model, Stephanie Allred Magleby

Theses and Dissertations

This thesis investigates the violation of Bell's Inequality through the use of nonlocal measurement schemes as encapsulated in a quasi-deterministic toy model. This toy model, called the Q Box, is reminiscent of Mermin's Box in that it describes a system that appears to be deterministic yet produces the statistics of a quantum type system. [1] The workings of the Q Box are detailed both as a thought experiment and as a computer simulation. Nonlocal measurement protocols similar to those which generate a violation of Bell's Inequality in the Q Box are also applied to Mermin's Box, with comparable results. [1] …