Master of Science, Miami University, 2009, Physics

We investigate entanglement in an open quantum system, specifically in bipartite and tripartite systems of two dimensions for weak and strong fields based on numerical calculations. We address a systematic approach in calculating a tripartite entanglement using concurrence as a measure of entanglement based on a direct detection scheme (quantum jump method - with and without knowledge of which qubit jumps). We are also numerically calculating entanglement using ‘Adiabatic Elimination' and the ‘Three-way tangle' or ‘Residual Entanglement' approaches. We present significant differences of the concurrences of the various bipartite splits among the results of two ways of direct detection scheme and when a phase is introduced in the coupling term of the energy.

Committee: Perry Rice PhD (Advisor); Samir Bali PhD (Committee Member); James Clemens PhD (Committee Member) Subjects: Physics

Doctor of Philosophy, The Ohio State University, 2020, Physics

In this thesis, we present a theoretical framework that can derive a general anyon theory for 2D gapped phases from an assumption on the entanglement entropy. We formulate 2D quantum states by assuming two entropic conditions on local regions, (a version of entanglement area law that we advocate). We introduce the information convex set, a set of locally indistinguishable density matrices naturally defined in our framework. We derive an isomorphism theorem and structure theorems of the information convex sets by studying the internal self-consistency. This line of derivation makes extensive usage of information-theoretic tools, e.g., strong subadditivity and the properties of quantum many-body states with conditional independence. The following properties of the anyon theory are rigorously derived from this framework. We define the superselection sectors (i.e., anyon types) and their fusion rules according to the structure of information convex sets. Antiparticles are shown to be well-defined and unique. The fusion rules are shown to satisfy a set of consistency conditions. The quantum dimension of each anyon type is defined, and we derive the well-known formula of topological entanglement entropy. We further identify unitary string operators that create anyon pairs and study the circuit depth. We define the topological $S$-matrix and show it satisfies the Verlinde formula. It follows that the mutual braiding statistics of the sectors are nontrivial (they are anyons); moreover, the underlying anyon theory is modular. Three additional things, closely related to this framework, are presented: (1) The framework on a discrete lattice; (2) A calculation of information convex set based on solvable Hamiltonians; (3) A conjecture concerning the generality of our assumptions.

Committee: Yuan-Ming Lu (Advisor); Stuart Raby (Committee Member); Daniel Gauthier (Committee Member); Mohit Randeria (Committee Member); David Penneys (Other) Subjects: Physics; Quantum Physics; Theoretical Physics

Master of Science, Miami University, 2024, Physics

Quantum entanglement – a strange correlation that can exist between quantum particles (irrespective of distance) where the measurement of the state of one particle instantaneously decides the state(s) of the other particle(s) has remained a central topic in the foundations of quantum mechanics since several decades. This phenomenon, which has no classical counterpart, has gained a renewed interest in recent decades when it was shown that entanglement can be used as an information resource in many quantum-enabled information technologies. This thesis focuses on studying the evolution of entanglement among quantum bits or qubits (building blocks in quantum information theory). In particular, under realistic conditions, we examine how different open quantum system models impact the dynamics and generation of entanglement when these qubits interact with their environment. To this end, using the machinery of quantum Langevin equations, input-output formalism, and master equations, we present a thorough analysis of free-space entanglement among qubits with vacuum-, Fock-, and thermal-state environments. Both entanglement dynamics and generation have been explored using a combination of analytic and numerical techniques.

Committee: Imran Mirza (Advisor); Edward Samson (Committee Member); Samir Bali (Committee Member); Caleb Eckhardt (Committee Member) Subjects: Physics

Doctor of Philosophy, The Ohio State University, 2024, Physics

In quantum many-body systems, fractionalization stands as a hallmark of quantum emergent phenomena, where an elementary degree of freedom, such as an electron, decomposes into distinct pieces with a fraction of quantum numbers due to frustration or strong quantum fluctuations. A canonical well-understood example of this is observed in one-dimensional quantum systems. In one-dimensional systems, the pronounced quantum fluctuations facilitate the deconfinement of these fractionalized quasiparticles, allowing them to exhibit independent dynamics, where electrons, carriers of both charge and spin, undergo spin-charge separation which results in the dynamical deconfinement of spinon and chargon. In two dimensions, however, the physics is more intricate. In the presence of frustrating interactions between spins, the interacting spins are unable to order. Instead, they create long-range patterns of entanglement leading to states of matter such as quantum spin liquids, heralding the topological quantum matter with novel fractionalized particles and emergent gauge fields. These states are characterized by topological order: ground state degeneracy on a manifold of non-zero genus, and fractionalized excitations with abelian and non-abelian quantum statistics. In these states, the original localized spin degrees undergo further fractionalization to give new degrees of freedom, such as Majorana fermions and spinons. In these states, both charges and spins are localized. However, the emergent fractionalized degrees of freedom can be remarkably delocalized and able to transport energy. Identifying and studying the phenomena of fractionalization presents a dual challenge: discerning fractionalized particles and finding material candidates that realize fractionalization. This dissertation presents a comprehensive theoretical study of fractionalization in both one and two dimensions, focusing on these challenges. In one-dimensional systems, we explore quantum and frustrated ma (open full item for complete abstract)

Committee: Nandini Trivedi (Advisor); Mohit Randeria (Committee Member); Marc Bockrath (Committee Member); Christopher Hirata (Committee Member) Subjects: Physics

Master of Science, Miami University, 2024, Physics

Entanglement generation and control, fundamental to many quantum information technologies such as quantum computing and quantum communications/networking, are the core of our research. We explore waveguide quantum electrodynamics (wQED), an exciting platform that enables strong light-matter interaction at the single photon and atom level. This thesis presents a comprehensive study on tripartite entanglement in bidirectional and uni-directional (chiral) wQED platforms. By incorporating realistic system conditions, including losses, we investigate how initially un-entangled two-level quantum emitters (qubits) can be entangled through waveguide-mediated fields composed of three-photon Fock states. We derive and apply Fock state master equations within the density matrix formalism of quantum optics. This work represents a crucial step towards analyzing multipartite entangled states in nanophotonic setups, a topic of growing interest in efforts to establish long-distance quantum networking, thereby underscoring the practical implications of our findings.

Committee: Imran Mirza (Advisor); Samir Bali (Committee Member); Burcin Bayram (Committee Member) Subjects: Physics

Bachelor of Arts (BA), Ohio University, 2024, Environmental Studies

Grassland birds have narrow habitat requirements that are influenced by food availability, habitat composition, and habitat structure. Because survival is influenced by habitat quality and availability, understanding habitat requirements is critical for conservation. I determined how Henslow's Sparrows (Centronyx henslowii) use grassland habitat in the breeding season. In the past 10 years, technology advancements have allowed researchers to study the habitat use and movement ecology of understudied birds, such as grassland birds. I deployed nanotags on 47 adult Henslow's Sparrows at two sites in southern Ohio to determine home range size and habitat use in relation to distance to edge and shrub, as well as the post-breeding dispersal and migratory timing. I predicted that Henslow's Sparrows would use core grassland habitat and avoid edge and shrubs. I found no difference in 95 % home range size between female (0.10 ± 0.03 ha) and male (0.32 ± 0.18 ha) Henslow's Sparrows. Henslow's Sparrows used shrubs when available and edge habitat as refugia after disturbance. I also found that Henslow's Sparrows use fields into August, past dates typically recommended for disturbance (e.g., mid to late July), which suggests the need to leave corridors and patches for refugia after management such as mowing or burning. I determined the fall migratory departure timing of 13 Henslow's Sparrows. I found that Henslow's Sparrows are at risk for entanglement which resulted in mortality of two birds. A third bird found entangled was found alive, entangled in vegetation, and was released after I removed the nanotag. I also found that 24 Henslow's Sparrows were able to remove nanotags and several damaged their nanotags. While I do not recommend the use of nanotags on this species in future studies, my study did result in determining fall migratory departure timing of Henslow's Sparrows in Ohio which was previously unknown.

Committee: Kelly Williams (Advisor) Subjects: Animals; Biology; Ecology; Environmental Studies; Organismal Biology; Wildlife Conservation; Wildlife Management; Zoology

MA, Kent State University, 2023, College of the Arts / School of Art

The patriarchal structure of education and the lack of political equitability calls for feminist(s) leadership as the opposing structure, where power thrives with the inclusion of others, and is informed by the sharing of others' lived experiences. This study aims to contribute to the active conversation of feminism(s) in the field of art education through a cross-generational examination of feminist(s) narrative experiences. Focusing on qualitative methods such as narrative inquiry, feminist ethnography, and arts-based educational research, data was collected through personal journaling, participant journaling, and a panel interview of six feminist-identifying art educators. The findings presented through data analysis coincide with current feminist(s) art educators' discussion of mentorship or co-mentorship, inclusive leadership and feminist(s) action, deconstruction of patriarchal curriculum, and continuous conversations across generations with a focus on reclaiming the joy and histories of feminism(s).

Committee: Linda Hoeptner Poling (Advisor); Juliann Dorff (Committee Member); Janice Kroeger (Committee Member) Subjects: Art Education

Doctor of Philosophy, The Ohio State University, 2022, Physics

Understanding and identifying quantum phases have been longstanding pursuits in the field condensed matter physics. The most exciting modern problems lie at the intersection of strong correlations and quantum information where highly entangled phases of matter are the most difficult to solve both analytically and computationally. The overarching aim of this thesis is to advance our understanding of strongly correlated materials in light of advanced, microscopic measurement techniques, capable of imaging and manipulating single qubits and measuring fascinating physics such as quantum entanglement. We begin our study with the Fermi-Hubbard model, a theoretical model that captures the insulating and conducting phases of high-temperature superconducting materials, and we end our discussion by characterizing novel quantum phases and dynamics realized on cutting-edge quantum simulation platforms. Our first focus is on the repulsive Fermi-Hubbard model. We elucidate the mechanism by which a Mott insulator transforms into a non-Fermi liquid metal upon increasing disorder at half filling. By correlating maps of the local density of states, the local magnetization, and the local bond conductivity, we find a collapse of the Mott gap toward a V-shape pseudogapped density of states that occurs concomitantly with the decrease of magnetism around the highly disordered sites, while the electronic bond conductivity increases. We propose that these metallic regions percolate to form an emergent non-Fermi liquid phase with a conductivity that increases with temperature. Our results provide one of the first microscopic investigations of dynamical response and how these two phases (correlated metal and Mott insulator) coexist microscopically and lead to an overall macroscopic phase transition. Our work provides novel predictions for electron conductivity measured via local microwave impedance combined with charge and spin local spectroscopies. Expanding beyond the ground state pr (open full item for complete abstract)

Committee: Nandini Trivedi (Advisor); Christopher Hirata (Committee Member); Jay Gupta (Committee Member); Ilya Gruzberg (Committee Member) Subjects: Condensed Matter Physics; Quantum Physics; Theoretical Physics

Master of Science, Miami University, 2021, Physics

The operation of state-of-the-art quantum computers are requiring the coherent control of 100's of quantum bits (qubits) to store, manipulate and transfer information quantum mechanically. The traditional theoretical tool adopted in the field of quantum optics such as the master equation approach, quantum Langevin equations, input-output formalism, and real-space method began to face challenges as these techniques are more suitable to deal with few qubit problems. Offering a solution to this issue, in this thesis, we present an introduction to the tensor network (TN) theory and Matrix Product States (MPS) as a formalism to predict ground states and time evolution of interesting excited states of many-qubit architectures. As a simple example, we apply the TN theory to waveguide quantum electrodynamics architectures to analyze the excitation dynamics of two-level quantum emitters coupled to the one-dimensional guided photonic modes.

Committee: Imran Mirza PhD (Advisor); Herbert Jaeger PhD (Committee Member); Samir Balli PhD (Committee Chair) Subjects: Information Science; Optics; Physics; Quantum Physics; Theoretical Physics

Doctor of Philosophy, The Ohio State University, 2018, Physics

In this dissertation, new ideas and methods from tensor network theory and neural network theory are discussed. Firstly, common computational methods, such as the exact diagonalization method, the Density Matrix Renormalization Group approach, and the tensor network theory are reviewed. Following this direction, a way of generalizing the tensor renormalization group (TRG) to all spatial dimensions is proposed. Mathematically, the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is discovered. A theoretical contraction framework is proposed. Furthermore, the canonical polyadic decomposition is introduced to tensor network theory. A numerical verification of this method on the 3-D Ising model is carried out. Secondly, this dissertation includes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction. Numerical examples are benchmarked and compared. Furthermore, highly entangled qubit states are searched for to show the applicability of this method. Finally, machine learning approaches are reviewed. Machine learning methods are applied to quantum mechanics. The radial basis function network in a discrete basis is used as the variational wavefunction for the ground state of a quantum system. Variational Monte Carlo(VMC) calculations are carried out for some simple Hamiltonians. The results are in good agreements with theoretical values. The smallest eigenvalue of a Hermitian matrix can also be acquired using VMC calculations. These results demonstrate that machine learning techniques are capable of solving quantum mechanical problems.

Committee: Yuan-Ming Lu Dr. (Advisor); Ciriyam Jayaprakash Dr. (Committee Member); Jay Gupta Dr. (Committee Member); Comert Kural Dr. (Committee Member) Subjects: Physics

Master of Arts, The Ohio State University, 2016, Anthropology

The U.S. Environmental Protection Agency defines environmental justice as “the fair treatment and meaningful involvement of all people… with regards to environmental policymaking” (EPA 2016). The idea that all people should be included in the decision-making process regarding their local environment reflects the democratic ideal of justice: that collective benefits are maximized when everyone has a say. However, in practice, this ideal is often messily implemented, and there are multiple structural barriers that impede some groups from fully participating in this process. Drawing on ethnographic fieldwork from a summer in Ashtabula County, Ohio, I investigate one such case—the Vincina Protocol Project—in which a group of grassroots environmental justice activists struggle to gain footing in the complex legal and scientific networks that surround environmental policymaking. I found that while ecological knowledge did play some role in activist proclivities, they actually rejected the label of environmentalist and filtered their message through an anthropocentric rhetoric that emphasizes the attachments between people and places as a condition for justice. I argue that the tendency for environmental scientists and policymakers to see such rural folk as Appalachian Ohioans as ignorant or uncaring ignores the material realities that prevent them from meeting the conditions of the democratic ideal, and investigate the ways in which this discourse further marginalizes Appalachian environmental justice activists. In concluding, I propose an alternative framework that considers society as part of nature in dealing with the multitude of social justice problems that plague rural communities across the United States.

Committee: Anna Willow Ph.D. (Advisor); Jennifer Syvertsen Ph.D., M.P.H. (Committee Member); Becky Mansfield Ph.D. (Committee Member) Subjects: Cultural Anthropology; Environmental Justice; Environmental Studies

BA, Oberlin College, 2004, Physics and Astronomy

The thesis documents the work done over the year to initiate an undergraduate Advanced Laboratory experiment which tests Bell's inequality. It provides reference theory for the experiment, including explanations of Bell inequalities, basics of nonlinear optics, type-I downconversion and entanglement, and polarization states of the entangled photons. A main result is the equipment and design proposal for the experiment, which will cost a total $19600, led in price by the $9000 of a four photodetector array and followed by the $5000 of a 405nm pump laser. Entangled photons are produced by pumping BBO in a two-crystal geometry. Although most of the light is transmitted, some undergoes type-I parametric downconversion. Degenerate pairs are in a tunable entangled state and can be used to show non-classical behavior. Specifically, a violation of the CHSH Bell inequality can be observed. Usable coincidence rates of several thousand per second are expected. Experimental and data analysis methods are described as the basis of future laboratory documentation. Explanations of equipment alignment and adjustment and data collection are included, as well as derivations of relevant analyses of the experimental data. Lastly the coincidence circuit built for the experiment is reviewed. The circuit costs less than $40 to construct and demonstrates a coincidence window of between 18ns and 36ns.

Committee: Stephen Fitgerald PhD (Advisor) Subjects: Experiments; Optics; Physics; Science Education

Master of Science, Miami University, 2005, Physics

We examine a cavity QED system comprised of a single atom, a driven cavity, and an optical lattice. Cavity decay, spontaneous emission, detunings, and Franck-Condon factors are all accounted for. We expand on previous work by releasing the harmonic approximation often used for the lattice and replacing it with Mathieu functions. The intensity-intensity and intensity-field correlation functions are examined in the weak-field limit in order to identify and explain non-classical properties therein.

Committee: Perry Rice (Advisor) Subjects:

Doctor of Philosophy, University of Akron, 2011, Polymer Science

Entangled polymeric liquids necessarily show significant nonlinear responses to fast and large external deformation. Recent particle-tracking velocimetric measurements showed that the nonlinear behavior may involve inhomogeneous shear. But even in absence of shear banding, it remains a challenge to characterize and establish a connection between various nonlinear rheological characteristics and the molecular rearrangements in the entanglement network. In this dissertation, the relationship between the dynamics of chain entanglement and the rheological behavior was studied under different deformation conditions. We emphasized with the present entangled polymeric liquids that nonlinearity in large amplitude oscillatory shear could arise due to rearrangement of their microstructures over time in response to large amplitude oscillatory shear. In this case, no correlation is obvious between strain dependence of the steady-state stress response and deviation of the steady-state stress from the sinusoidal wave. We investigated the nature of steady shear flow of entangled polymeric liquids by superimposing either small amplitude oscillatory shear or small step strain and analyzing the resultant mechanic responses. Our results showed that a) polymer dynamics (in terms of stress relaxation) were accelerated relative to the quiescent dynamics in direct proportion to the underlying shear rate, and b) the steady shear was a viscous state where chains were displaced past one another on a time scale comparable to the reciprocal rate, consistent with the idea of convective constraint release (CCR). We carried out rate-switching tests to further elucidate the changes of the transient strength of chain entanglement in response to various forms of shearing. Our results showed that a) elastic yielding could occur during quiescent relaxation after a large step strain, b) the new state of chain entanglement was stable for a significant period after shear cessation from steady state, an (open full item for complete abstract)

Committee: Shi-Qing Wang Dr. (Advisor); Gustavo Carri Dr. (Committee Member); Gary Hamed Dr. (Committee Member); Darrell Reneker Dr. (Committee Member); Robert Weiss Dr. (Committee Member) Subjects: Polymers

Doctor of Philosophy, University of Akron, 2006, Political Science

A central task in polymer rheology is to search for constitutive equations that relate the flow field with the corresponding stress field in both transient and steady states. A parallel objective is to determine the state of chain conformation as a function of the flow condition. In disagreement with previous studies, our experimental data show that entangled monodisperse polymers respond differently to the applied shear strain and shear stress. In conventional shear strain rate controlled measurement, entangled polymers result in a stress plateau well known as shear thinning while a constitutive entanglement-disentanglement transition takes place when sheared under stress-controlled mode. Direct visualization of the velocity field with particle tracking velocimetry and flow birefringence reveals that entangled polymeric fluids develop non-homogeneous flow field across velocity gradient direction when sheared under rate-controlled mode. Lack of uniform shear deformation is observed when these fluids are subjected to large amplitude oscillatory shear at frequencies beyond overall chain relaxation rate. The combination of rheometry, rheo-optics and particle tracking velocimetry has led to the discovery of an entanglement-disentanglement transition in shear stress mode and the presence of a shear rate gradient across sample thickness in shear rate controlled mode. These first results may provide a reliable phenomenological basis for the future development of a realistic description of nonlinear polymer rheology.

Committee: Shi-Qing Wang (Advisor) Subjects: